Calc

Evaluate the integral by reversing the order of integration.

(2 integrations)
0 to 1
sqrt(x) to 1

8(y^3+1) dy dx

  1. 👍
  2. 👎
  3. 👁
  1. ∫[0,1]∫[√x,1] 8(y^3+1) dy dx
    = ∫[0,1]8(y^4/4+y)|[√x,1] dx
    = ∫[0,1]8[(1/4+1)-(x^2/4+√x)] dx
    = ∫[0,1] -2x^2 - 8√x + 10 dx
    = (-2/3 x^3 - 16/3x^(3/2) + 10x [0,1]
    = -2/3 - 16/3 + 10
    = 4

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus integrals

    Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) integral x^5/x^6-5 dx, u = x6 − 5 I got the answer 1/6ln(x^6-5)+C but it was

  2. calculus

    1.Evaluate the integral. (Use C for the constant of integration.) integral ln(sqrtx)dx 2. Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given axis. y =

  3. calculus

    Make a substitution to express the integrand as a rational function and then evaluate the integral. (Use C for the constant of integration.) 1/x{(x-1)^1/2} dx

  4. calculus

    Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) (x^2−x+12)/(x^3+3x) dx

  1. calc

    evaluate the integral: y lny dy i know it's integration by parts but i get confused once you have to do it the second time Leibnitz rule (a.k.a. product rule): d(fg) = f dg + g df y lny dy = d[y^2/2 ln(y)] - y/2 dy ----> Integral

  2. Calculus Please Help2

    Evaluate the integral by using substitution. Use an upper-case "C" for the constant of integration. integral x^5((x^6-2)^10)dx ty

  3. Calculus

    Find the exact coordinates of the centroid. y = sqrt[x], y = 0, x = 9. -------------- Is this basically 1/4 of an oval/ellipse? If so then the area would be: pi*9*3, correct? So the X coordinate would equal: 1/Area * Integral from

  4. Calc 1

    Evaluate the integral by making the given substitution. (Use C for the constant of integration.) ∫ dt/(1-7)^7, u=1-7t

  1. calculus

    Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) (11)/(x^3-125) dx

  2. Calculus

    Graph the curve and find its exact length. x = e^t + e^-t, y = 5 - 2t, from 0 to 3 Length = Integral from 0 to 3 of: Sqrt[(dx/dt)^2 + (dy/dt)^2] dx/dt = e^t - e^-t, correct? dy/dt = -t^2 - 5t, correct? So: Integral from 0 to 3 of

  3. Calc

    Evaluate the integral by reversing the order of integration. (2 integrals) 0 to 8 cube root(y) to 2 8e^(x^4) dx dy

  4. Calculus

    A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 80 ft is given by the following. y = 150 - (1/40)(x-50)^2 Find the distance traveled by the kite. y = 150 - (1/40)(x-50)^2 y

You can view more similar questions or ask a new question.