integral of below.

ſ√y . e^-y^3​

Answers

Answer 1

Assuming you're equipped with the error function,

[tex]\mathrm{erf}(x)=\displaystyle\frac2{\sqrt\pi}\int_0^x e^{-u^2}\,\mathrm du[/tex]

whose derivative is

[tex]\dfrac{\mathrm d}{\mathrm dx}\mathrm{erf}(x)=\dfrac2{\sqrt\pi}e^{-x^2}[/tex]

by substituting x = √y, so that x ² = y and 2x dx = dy, we have

[tex]\displastyle\int\sqrt y e^{-y^3}\,\mathrm dy=\int 2x^2 e^{-x^6}\,\mathrm dx[/tex]

Then if u = x ³ and du = 3x ² dx, we have

[tex]\displaystyle\int\sqrt y e^{-y^3}\,\mathrm dy=\int\frac23 e^{-u^2}\,\mathrm du[/tex]

[tex]\displaystyle\int\sqrt y e^{-y^3}\,\mathrm dy=\frac{\sqrt\pi}3\mathrm{erf}(u)+C[/tex]

[tex]\displaystyle\int\sqrt y e^{-y^3}\,\mathrm dy=\frac{\sqrt\pi}3\mathrm{erf}(x^3)+C[/tex]

[tex]\displaystyle\int\sqrt y e^{-y^3}\,\mathrm dy=\boxed{\frac{\sqrt\pi}3\mathrm{erf}\left(y^{\frac32}\right)+C}[/tex]

If you're not familiar with the error function, unfortunately there is no elementary antiderivative...


Related Questions

Six out of the 12 members of the school choir are boys. In simplest form, what fraction of the choir is boys?

Answers

Answer:

1/2

Step-by-step explanation:

reflect point a (1,1) over y axis

Answers

The answer is -1, 1.

Answer:

reflected across the y axis, the point (1, 1) becomes (-1, 1).

Step-by-step explanation:

To reflect a point across the y-axis, all you need to do is negate the x coordinate.  That gives you (-1, 1)

Randy purchases a cap for $12. The store charges him 7% sales tax on the purchase. How much sales tax will the store charge on the purchase?

Answers

$ 12.84 because first you want to convert the 7% into a decimal which is 0.07 and then multiply 12 x 0.07 = 0.84 then add 0.84 + 12 = 12.84

Answer:The answer is (D)

Step-by-step explanation:Just took he quiz

the answer is 5.
22. What is the minimum speed needed to travel at least 440 miles in 8 hours? Choose and
justify a solution (54 mph, 55 mph, 56 mph)

Answers

Answer:

440ml divide 8hrs = 55mph

1. What is 5% of 224?

Answers

Answer:

11.2

Step-by-step explanation:

224 x 0.05 = 11.2

Hope this helped!

i believe it is 12.2  

One-third of the total number of marbles in a jar are blue and green. There are 24 blue marbles and 18 green marbles. How many marbles are in the jar?

Answers

Answer:

126 marbles

Step-by-step explanation:

if 42 is 1/3 of the jar, times it by 3 and that's the total.

Answer:

126 marbles

Step-by-step explanation:

24 - blue

18 - green

42 are blue or green

let 't' = total number of marbles

1/3t = 42

t = 42 x 3 = 126

What transformation has occurred

Answers

Answer:

Step-by-step explanation:

distributive

Please see the attachment. Thank you

Answers

I think second and third

which equation represents a line parallel to the y axis?

A: y=x
B: x=4
C: y=4
D: y=x+4

Answers

B: x=4 hope this helped!!

1. Which of the following is an irrational number?
A. 3
B. 3.666...
C. 19
D. Vg

Answers

Answer:

Vg

Step-by-step explanation:

All the others are decimals

pls give thanks, 5 star, brainliest

i’m thinking B but not too sure

A railroad car container can hold​ 66,000 pounds. Mr. Evans wants to ship 80 ovens and some freezers in the same container. If each freezer weighs 600​ pounds, how many freezers could be shipped in the​ container. Each oven
weighs
300 pounds

Answers

Answer:

70 freezers

Step-by-step explanation:

Each oven weights 300 pounds and there 80 ovens:

80*300 = 24000 pounds

Weight left for freezers:

66000 - 24000 = 42000 pounds

Number of freezers could be added:

42000/600 = 70

EMERGENCY!!!!

I have fallen and can't get up.

Answers

Answer:

do you need a bandaid?

Step-by-step explanation:

Step-by-step explanation:

Wth?

Are u okay??

call 911

You spent 25% of your monthly wages on rent. If you earned $75,350 last year,
how much did you spend on rent each month?

Answers

1,569.79 a month. 75,250x0.25= 18,837.50 a year.
18,837.5/12= 1,569.79 a month.

what is F?
H is 5m
I is 8m
G is 10m

Answers

Answer: F is 11m.

Step-by-step explanation: Because H,I,G are all increasing their numbers like plus 3, plus 2, and the last one has to be plus 1.

What’s the answer? I have to pass with my credits for high school

Answers

-0.2 or -1/5
I would use -1/5 cause it’s a fraction

Can u guys help me quick plz I will make brainliest (I need help with 32)plzzzz

Answers

Answer:

A

Step-by-step explanation:

Find the slope of the line that passes through (3,-7) and (-6,5).

Answers

Answer:

9,12?

Step-by-step explanation:

"" Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (0, 11, −9) and parallel to the line x = −1 + 3t, y = 6 − 3t, z = 3 + 7t

Answers

Find the tangent vector T to the given line (t) = 〈 x(t), y(t), z(t) 〉, with parametric equations,

x(t) = -1 + 3t

y(t) = 6 - 3t

z(t) = 3 + 7t

by differentiating (t) component-wise:

T = '(t) = 〈 dx(t)/dt, dy(t)/dt, dz(t)/dt

T = 〈3, -3, 7〉

Scale T by any real number t to get the line through the origin (when t = 0) and the point (3, -3, 7) (when t = 1), which of course runs parallel to '(t). This gives the vector tT. Translate this by any vector v = 〈a, b, c〉 to force this line to pass through the point (a, b, c) instead of the origin, while still remaining parallel. You want the new line to pass through (0, 11, -9), so take v = 〈0, 11, -9〉.

Then the vector equation of the new line is

tT + v = t 〈3, -3, 7〉 + 〈0, 11, -9〉 = 〈3t, 11 - 3t, -9 + 7t

with parametric equations

x(t) = 3t

y(t) = 11 - 3t

z(t) = -9 + 7t

A closed box has a square base with side length feet and height feet. Given that the volume of the box is cubic feet, express the surface area of the box in terms of only.

Answers

Complete Question:

A closed box has a square base with side length L feet and height h feet. Given that the volume of the box is 39 cubic feet, express the surface area of the box in terms of L only.

Answer:

[tex]A = \frac{156}{L} + 2L^2[/tex]

Step-by-step explanation:

Given

[tex]Volume = 39ft^3[/tex]

Required

Express the surface area in terms of L

Because the box has a square base:

The volume is:

[tex]Volume = Base\ Area * Height[/tex]

Where

[tex]Base\ Area = L * L[/tex]

So, we have:

[tex]Volume = L * L * H[/tex]

Substitute 39 for Volume

[tex]39= L * L * H[/tex]

[tex]39= L^2 * H[/tex]

Make H the subject

[tex]H = \frac{39}{L^2}[/tex]

The surface area (A) of a box with square base is:

[tex]A = 2(LH + LH + L^2)[/tex]

[tex]A = 2(2LH + L^2)[/tex]

Open bracket

[tex]A = 4LH + 2L^2[/tex]

Substitute [tex]\frac{39}{L^2}[/tex] for H

[tex]A = 4L * \frac{39}{L^2} + 2L^2[/tex]

[tex]A = \frac{4L *39}{L^2} + 2L^2[/tex]

[tex]A = \frac{4*39}{L} + 2L^2[/tex]

[tex]A = \frac{156}{L} + 2L^2[/tex]

James can eat 12 jelly beans per minute, and Jenny can eat 8 jelly beans per minute. How
many minutes will it take Jenny and James to eat a combined total of 100 jellybeans?

Answers

Answer:

5 mins.

Step-by-step explanation:

hope his helps good luck

Answer:

5 minutes

Step-by-step explanation:

A frozen yogurt shop has a combination of 150 small and medium sized bowls on their counter. Each small bowl hold 4 ounces and each medium bowl holds 6 ounces. If the bowls on the counter will hold a total of 764 ounces, find the number of small and medium sized bowls on the counter

Answers

77 small and 76 medium

The number of small sized bowls on the counter = 68 bowls

The number of medium sized bowls on the counter = 82 bowls

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of small bowls on the counter be = x

Let the number of medium bowls on the counter be = y

The total number of bowls is = 150

So , the equation will be

x + y = 150   be equation (1)

The amount the small bowl can hold = 4 ounces

The amount the medium bowl can hold = 6 ounces

The total amount of all the bowls on the counter = 764 ounces

So , the equation will be

4x + 6y = 764   be equation (2)

Now , on simplifying the equation (1) and equation (2) , we get

Multiply equation (1) by 4 , we get

4x + 4y = 600   be equation (3)

Subtracting equation (3) from equation (2) , we get

2y = 164

Divide by 2 on both sides , we get

y = 82

Therefore the number of medium sized bowl is 82 bowls

Substituting the value of y in equation (1) , we get

x + y = 150

x + 82 = 150

Subtracting 82 on both sides , we get

x = 68

Therefore , the number of small sized bowl is 68 bowls

Hence ,

The number of small sized bowls on the counter = 68 bowls

The number of medium sized bowls on the counter = 82 bowls

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Evaluate: (4x¹⁴)(8x¹¹) *​

Answers

Answer:

32x^25

Step-by-step explanation:

4x^14*8x^11

inequalities of x + 9 < 12 I need help solving this

Answers

the inequality would be x>3

Use the discriminant to describe the roots of each equation. Then select the best description.

2 = x2 + 5x

double root
real and rational root
real and irrational root
imaginary root

Answers

ExplanationGiven the equation.

[tex]2 = {x}^{2} + 5x[/tex]

Arrange the expression into the standard form.

[tex]0 = {x}^{2} + 5x - 2 \\ {x}^{2} + 5x - 2 = 0[/tex]

Discriminant

From the standard form equation and from the given equation.

[tex]a {x}^{2} + bx + c = 0 \\ a = 1 \: \: \: b = 5 \: \: \: c = - 2[/tex]

Discriminant Formula

[tex]D = {b}^{2} - 4ac[/tex]

Substitute the value of terms in the discriminant formula.

[tex]D = {(5)}^{2} - 4(1)( - 2) \\ D = 25 - 4( - 2) \\ D = 25 + 8 \\ D = 33[/tex]

Discriminant Types

[tex]D > 0 \: \: \: \: 2 \: \: real \: \: roots \\ D = 0 \: \: \: \: 1 \: \: real \: \: root \\ D < 0 \: \: \: imaginary \: \: roots[/tex]

We can rule out the Imaginary root and double root because the discriminant is greater than 0. Therefore, the only choices are either Irrational or Rational.

However, we cannot factor the expression by using two brackets or common factor. We can say that the equation has two real irrational roots.

Answerreal and irrational root
x2+5x-2=0
a=1, b=5, c=-2

b2-4ac is the discriminant.
(5^2)-4(1)(-2)
25+8=33, so the discriminant is positive

This means there are two real rational roots, so the answer is the second option

7. What is the slope of the line that passes through the pair of points (2, 5) and (8, 3)?

A. 1/3

B. -1/3

C. 3

D.-3

Answers

Answer:

c

Step-by-step explanation:

irrational numbers are closed under subtraction true/false

Answers

Answer:

False

Step-by-step explanation:

a+(-a)=a-a = 0 which means irrational numbers are not closed under addition or subtraction.

False. Irrational numbers are not closed under subtraction.

Given data:

Closure under subtraction means that if you subtract two irrational numbers, the result will always be another irrational number.

However, this is not true for irrational numbers.

For example, consider the irrational numbers √2 and √2 + √2. Both of these numbers are irrational. However, when we subtract √2 from √2 + √2, we get:

(√2 + √2) - √2 = √2

The result, √2, is still an irrational number. But if we subtract two irrational numbers like √2 from √2, we get:

√2 - √2 = 0

The result, 0, is a rational number, not an irrational number.

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Suppose that quiz scores in a beginning statistics class have a mean of 6.6 with a standard deviation of 0.6. Using Chebyshev's Theorem, what is the minimum percentage of quiz scores between 4.8 and 8.4

Answers

Answer:

88.89%

Step-by-step explanation:

Calculation for what is the minimum percentage of quiz scores between 4.8 and 8.4

The calculated minimum percentage value of quiz scores between

First step is to calculate the lower k value using this formula

k=(x1−m)/s

Where:

x1 represent first random value 4.8

x2 represent second random value 8.4

m represent mean 6.6

s represent standard deviation 0.6

Let plug in the formula

k=(4.8−6.6)/0.6

k=−1.8/0.6

k=−3

Second step is to calculate the upper k value

k=(x2−m)/s

k=(8.4−6.6)/0.6

k=1.8/0.6

k=3

Now let calculate the minimum percentage

Using this formula

Minimum percentage=1−1/k^2

Let plug in the formula

Minimum percentage=1−1/3^2

Minimum percentage=1−1/9

Minimum percentage=1−0.1111

Minimum percentage=0.8889*100

Minimum percentage=88.89%

Therefore the minimum percentage of quiz scores between 4.8 and 8.4 is 88.89%

Answer:

75%

Step-by-step explanation:

5.2−6.40.6=−2  and 7.6−6.40.6=2.

This means that 5.2 lies 2 standard deviations below the mean and 7.6 lies 2 standard deviations above the mean.

According to Chebyshev's Theorem, at least 75% of data values lie within 2 standard deviations of the mean.

Therefore, we can say that 75% is the minimum percentage of quiz scores between 5.2 and 7.6.

WG-W Online Textboo
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Homework 6.4-6.6
Question 8 of 13 (1 point) | Question Attempt: 1 of Unlimited
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The Watson family and the Nelson family each used their sprinklers last summer. The water output rate for the Watson family's sprinkler was 35 L per hour. The
water output rate for the Nelson family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 60 hours, resulting in a total
water output of 1700 L. How long was each sprinkler used?
Note that the ALEKS graphing calculator can be used to make computations easier.

Answers

Answer:

We have two variables W and NW= 35 L N = 25L Total: 60 hrs respectfully between W and N Total Water: 1700 L 35W + 25N = 1700 (1)W + N = 60 (2)Just substitute!N = 60 + W 35W + 25(60 + W) = 170035 W + 1500 + 25W = 170060W + 1500 = 170060W = 200 W = 3.33 Now solve for N

Drag the point A to the location indicated in each
scenario to complete each statement.

Answers

Answer:

The answer is...

1: quadrant III

2: quadrant II

3: quadrant IV

4: quadrant I

Step-by-step explanation:

If A is in quadrant |, and is multiplied by a negative scalar C, CA is in Quadrant |||, If A is in quadrant ||, and is multiplied by a positive scalar C, CA is in Quadrant ||, If A is in quadrant ||, and is multiplied by a  negative scalar C, CA is in Quadrant |V and If A is in quadrant ||I, and is multiplied by a  negative scalar C, CA is in Quadrant |.

What is Coordinate system?

Coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points.

The point A to the location indicated in each scenario.

If A is in quadrant |, and is multiplied by a negative scalar C, CA is in Quadrant |||

If A is in quadrant ||, and is multiplied by a positive scalar C, CA is in Quadrant ||

If A is in quadrant ||, and is multiplied by a  negative scalar C, CA is in Quadrant |V

If A is in quadrant ||I, and is multiplied by a  negative scalar C, CA is in Quadrant |.

Hence, A is in quadrant |, and is multiplied by a negative scalar C, CA is in Quadrant |||, If A is in quadrant ||, and is multiplied by a positive scalar C, CA is in Quadrant ||, If A is in quadrant ||, and is multiplied by a  negative scalar C, CA is in Quadrant |V and If A is in quadrant ||I, and is multiplied by a  negative scalar C, CA is in Quadrant |.

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use substitution X+y=11 -x=-y-9​

Answers

Answer:

-(_y)-11=-y-9

Y-11=-y-9

2y=2

Y=1

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