# calculus

Assuming that:

Definite Integral of e^(-x^2) dx over [0,infinity] = sqrt(pi)/2

Solve for

Definite Integral of e^(-ax^2) dx over [-infinity,infinity]

I don't know how to approach the new "a" term. I can't use u-substitution, integration by parts, partial fractions, or trig substitution. How do I do this?

1. 👍
2. 👎
3. 👁
1. Substitute x = t/sqrt(a). The integral then becomes:

a^(-1/2)Integral of e^(-t^2) dt over [-infinity,infinity] =

2 a^(-1/2)Integral of e^(-t^2) dt over [0,infinity] = sqrt(pi/a)

1. 👍
2. 👎

## Similar Questions

1. ### Calculus

Write the limit as n goes to infinity of the summation from k equals 1 of the product of the 4th power of the quantity negative 1 plus 3 times k over n and 3 over n as a definite integral.

2. ### calculus (please with steps and explanations)

consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each

Find the range of the function F(x)= definite integral from [-6,x] of sqrt(36-t^2)dt. [0, 36π] [0, 18π]*** [-6, 6] [-6, 0]

4. ### calculus

Evaluate lim (1³ +2³ +3³ +…+ n3)/n^4 n →∞ by showing that the limit is a particular definite integral and evaluating that definite integral.

1. ### ap calculus

Which of the following definite integrals gives the length of y = e^(e^x) between x=0 and x=1? All the answers are preceded by the integral sign from 0 to 1. (a) sqrt[1 + e^(2*(x+e^x))] dx (b) sqrt[1 + e^(4x)] dx (c) sqrt[1 +

2. ### definite integral

Use the Riemann Sums corresponding to 5 inscribed rectangles of equal width to approximate the integral a= 1, b= 3, (1/x)dx this is all for definite integral i just know x1=1.4, x2=1.8, x3=2.2, x4=2.6, x5=3.0 how do i continue

3. ### Calculus

Find the definite integral that represents the arc length of the curve y=sqrt(x) over the interval [0, 3]

4. ### Calculus (urgent help)

consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each

1. ### calculus

consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each

2. ### Calculus

Set up a definite integral (but do not evaluate it!) for the area of the surface obtained by rotating the curve y =x^3/3 , 0 ≤ x ≤ 1, about the x-axis. The integral should contain only one variable (x or y).

3. ### Math emergency I have 10 minutes to submit it.

Evaluate the definite integral. x sqrt(13 x^2 + 36)dx between (0,1)

4. ### Math

Write the limit as n goes to infinity of the summation from k equals 1 of the product of the 10th power of the quantity 5 plus 2 times k over n and 2 over n as a definite integral.