Use your calculator to find the approximate volume in cubic units of the solid created when the region under the curve y = sin(x) on the interval [0, π] is rotated around the x-axis.

Question

Question options:

1)	4.93
2)	1.57
3)	6.28
4)	2.00

Answer 1

Hi

The answer is 4.93

explain:

V = π* ∫sin²x dx bounded 0 to π

as you know sin²x = ( 1- cos2x )/2 by replace in integral you will have:

V = π * ∫1- cos2x )/2 dx = π /2 *∫ (1- cos2x )dx = π /2 * ( x - 1/2 sin2x) bounded 0 to pi

V = pi / 2 * ( pi - 1/2 sin2pi - 0 +1/2 sin 2*0)

V = pi / 2 * ( pi - 0 - 0 - 0 )

V = pi * pi /2 = 3.14 * 3.14 /2 = 4.9298 after rounded = 4.93

I hope it is useful.

Answer 2

The answer is pi²/2 = 4.93