calculus

1. Find the volume V obtained by rotating the region bounded by the curves about the given axis.
y = sin(x), y = 0, π/2 ≤ x ≤ π; about the x−axis
2. Find the volume V obtained by rotating the region bounded by the curves about the given axis.
y = 3 sin2(x), y = 0, 0 ≤ x ≤ π; about the x−axis

I am struggling with the setup.

  1. 👍 0
  2. 👎 0
  3. 👁 431
  1. You want
    Volume = π∫ sin^2 x dx from π/2 to π

    the hard part is to integrate sin^2 x
    start with : cos (2x) = 1 - 2sin^2 x
    2sin^2 x = 1 - cos(2x)
    sin^2 x = 1/2 - (1/2)cos(2x)
    so ∫ sin^2 x dx = (1/2)x - (1/4)sin(2x)

    Volume = π∫ sin^2 x dx from π/2 to π
    = π[ (1/2)x - (1/4)sin (2x) ] from π/2 to π
    = π( π/2 - (1/4)(0) - (π/4 - (1/4)(0) ) )
    = π(π/4)
    = π^2/4

    In the next one you will have to integrate sin^4 x
    there are many videos showing you how to do that,
    here is "blackpenredpen's " version
    https://www.youtube.com/watch?v=SCQdKorKbKM

    1. 👍 0
    2. 👎 0
    👨‍🏫
    Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 8 sin x, y = 8 cos x, 0 ≤ x ≤ π/4; about y = −1

  2. Calculus

    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y= 2e^(−x), y= 2, x= 6; about y = 4. How exactly do you set up the integral? I know that I am supposed to use

  3. Calculus

    a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y =

  4. calculus

    1. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(5x), y = 1, y = 3, x = 0; about the y-axis 2. Use the method of cylindrical shells to find the volume V

  1. calculus review please help!

    1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate,

  2. calculus

    Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips

  3. Calculus

    Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(x), y=0, x=0, and x=π/2 about the line y=1.

  4. Cal 2

    Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves y=3/(1+x^2), y=0, x=0, and x=2 about the line x=4. Volume =

  1. Calculus II

    Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. y = ln x, y = 4, y = 5, x = 0 Find the volume V of this solid. Help!!! Thank you in advance :(

  2. calculus

    Find the volume of the solid obtained by rotating the region bounded by the curves y = x^8, y = 1 about the line y = 5.

  3. calc

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0, y=cos(7x) , x=π/14, x=0 about the axis y=−8

  4. calculus

    Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy = 2, x = 0, y = 2, y = 4

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