Consider the curve defined implicitly by

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

Problem

2xy + y^{2} = 8

. Let

S

be the region bounded by this curve, the

y

-axis, and the horizontal lines

y=1

and

y=2

. Which of the following is the exact area of

S

? (a)

4\ln 2 + \dfrac{3}{4}

(b)

4\ln 2 - \dfrac{3}{2}

(c)

4\ln 2 - \dfrac{3}{4}

(d)

2\ln 2 - \dfrac{3}{4}