Math

posted by .

If f(x) is an anti-derivative (i.e. primitive) of x*e^(-x^2) and f(0)=1. Then f(1)=?

  • Math -

    let u = x^2
    we have
    f = 1/2∫e^-u du
    f(x) = -1/2 e^(-x^2) + C

    1 = -1/2 (1) + C
    C = 3/2

    f(x) = -1/2 e^(-x^2) + 3/2
    f(1) = -1/2 * 1/e + 3/2
    = 1/2 (3 - 1/e)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc

    find the area between the x-axis and the graph of the given function over the given interval: y = sqrt(9-x^2) over [-3,3] you need to do integration from -3 to 3. First you find the anti-derivative when you find the anti-derivative …
  2. anti derivative

    please help me find anti derivative of -sinx * cos^2x am i using integration by parts?
  3. math

    How do you find the anti derivative of: [(e^x^2-2x)/(e^x^2)] ?
  4. calc

    i did this problem and it isn't working out, so i think i'm either making a dumb mistake or misunderstanding what it's asking. A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is given …
  5. calculus

    Find the anti-derivative of x^4... Isn't it 4x^3+c?
  6. math

    what is the anti-derivative of cos^5x
  7. Calculus

    Find the anti derivative of u^-2(1-u^2+u^4)du. Need steps so I can try to grasp this. Thanks. I couldn't figure out how to write the anti deriv. symbol but it is in front on the u^-2. Thanks
  8. Calculus

    Find the anti derivative of the following: 1. u^-2(1-u^2+u^4)du 2. (sqrt(x)+ 3/x - 2e^(x))dx The anti derivative symbol is in front of the equations. Also need help on find f(x) so that it satisfies f'(x) = 1+e^x+1/x and f(1) = 3+e. …
  9. Calculus

    Find the anti-derivative of the integral [(7t^2+6t-15)/t^4]dt
  10. Calculus

    Find the anti derivative for 4/(x^2+1)

More Similar Questions