Question 6(3 points)

LetRbe the region between the graph of the functiony= sinxand thex-axis, 0

{"version":"1.1","math":"$\le$"}x

{"version":"1.1","math":"$\le$"}

{"version":"1.1","math":"$\mathrm{\pi }$"}.By the cylindrical shell method, the volume of the solid obtained by revolvingRabout the linex=

{"version":"1.1","math":"$-$"}

{"version":"1.1","math":"$\mathrm{\pi }$"}can be calculated by

Question 6 options:

a)

0

(

2

sin

2

x)dx

{"version":"1.1","math":"\(\pi\int_0^\pi (\pi^2-\sin^2{x})dx\)"}

b)

2

0

(x)sin

2

xdx

{"version":"1.1","math":"\(2\pi\int_0^\pi (\pi-x) \sin^2{x}dx\)"}

c)

2

0

(x+)sin

2

xdx

{"version":"1.1","math":"\(2\pi\int_0^\pi (x+\pi)\sin^2{x}dx\)"}

d)

0

(x+)sinxdx

{"version":"1.1","math":"\(\pi\int_0^\pi (x+\pi)\sin{x}dx\)"}

e)

2

0

(x)sinxdx

{"version":"1.1","math":"\(2\pi\int_0^\pi (\pi-x)\sin{x}dx\)"}

f)

2

0

(x+)sinxdx

Question 6 (3 points) Let R be the region between the graph of the function y = sin x and the x-axis, 0 _ x _ It. By the cylindrical shell method, the volume of the solid obtained by revolving R about the line x = -It can be calculated by Oan Jo" (72 - sin x)dx Ob) 2n ." (x - x) sin xdx Ocan " (x + ) sin xdx Odtf" (x + ) sinxdx Oe) 2n fo" (x - x) sin xdx Of) 2n / (x + 7) sin xdx