Let , and be the roots of the equation . Then, the area bounded by the curves , the…

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

Problem

Let

f(x) = x^2

g(x) = \cos x

and

\alpha, \beta (\alpha < \beta)

be the roots of the equation

18x^2 - 9\pi x + \pi^2 = 0

. Then, the area bounded by the curves

y = f \circ g(x)

, the ordinates

x = \alpha, x = \beta

and the

X

-axis is (1)

\frac{1}{2}(\pi - 3)

sq units (2)

\frac{\pi}{3}

sq units (3)

\frac{\pi}{4}

sq units (4)

\frac{\pi}{12}

sq units