Question

Help please. Evaluate the integral by making the given substitution. The integral of xe^(-x^2/2) dx with u=-x^2/2

Answer 1

du = -x, so you can rewrite the integral as:

\[-\int\limits e^u du\]

Do you see how to do it from there?

Answer 2

I understand that part, but the next step is what i do not understand. Could you work it out please?

Answer 3

Oh, sorry. After that, you find the antiderivative, which is just e^u, and then add in the negative sign, so -e^u. Then, you know that u=-x^2/2, so it's -e^(-x^2/2)+C.

Answer 4

Do you see how that works?

Answer 5

I see. Thank you. Also for the -x^2/2, the 2s can cancel out right? which is why its just -x?

Answer 6

Right, the 2's cancel when you take the derivative.

Answer 7

cool cool. thank you so much. you are very helpful.

Answer 8

No problem.