# 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
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

1. 👍 0
2. 👎 0
👨‍🏫
Reiny

## 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) 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