Let be the region enclosed by the graphs of and between their points of intersection…

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

R

be the region enclosed by the graphs of

y = \cos x

and

y = x

between their points of intersection in the interval

0 \le x \le \dfrac{\pi}{2}

. When

R

is revolved about the

x

-axis, which of the following integrals represents the volume of the resulting solid? (The intersection points occur at

x = 0

and

x \approx 0.74

.) (a)

V = \pi \displaystyle\int_{0}^{0.74} \bigl[x^{2}-(\cos x)^{2}\bigr]\,dx

(b)

V = \pi \displaystyle\int_{0}^{\pi/2} \bigl[(\cos x)^{2}-x^{2}\bigr]\,dx

(c)

V = \pi \displaystyle\int_{0}^{0.74} \bigl[(\cos x)^{2}-x^{2}\bigr]\,dx

(d)

V = \pi \displaystyle\int_{0}^{0.74} \bigl(\cos x-x\bigr)^{2}\,dx