For the region bounded by the curves and

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

For the region bounded by the curves

x = y^{2} - 4y

and

x = y + 2

, which statement best explains why integrating with respect to

y

is more convenient than integrating with respect to

x

when finding the area of the region? (a) Because integrating with respect to

y

eliminates the need to solve a quadratic equation for

y

in terms of

x

. (b) Because integrating with respect to

y

makes the integrand linear rather than quadratic, which is simpler to integrate. (c) Because for every value of

y

in the region the left and right boundaries are given by single functions of

y

, whereas vertical slices would intersect the region in more than one segment. (d) Because integrating with respect to

x

would produce negative limits of integration, which cannot be used when computing area.