When a region is bounded on the right by for but its left boundary changes from to at

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

Problem

When a region is bounded on the right by

x=h(y)

for

a\le y\le b

but its left boundary changes from

x=f(y)

x=g(y)

y=c\;(a<c<b)

, which of the following correctly represents the area of the region in terms of definite integrals with respect to

y

? (a)

\displaystyle \int_{a}^{c}\bigl(h(y)-f(y)\bigr)\,dy+\int_{c}^{b}\bigl(g(y)-h(y)\bigr)\,dy

(b)

\displaystyle \int_{a}^{b}\bigl(h(y)-f(y)\bigr)\,dy

(c)

\displaystyle \int_{a}^{c}\bigl(h(y)-f(y)\bigr)\,dy+\int_{c}^{b}\bigl(h(y)-g(y)\bigr)\,dy

(d)

\displaystyle \int_{a}^{b}\bigl(h(y)-g(y)\bigr)\,dy