Let and be continuous functions that intersect only at on the interval

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

Problem

Let

r

and

s

be continuous functions that intersect only at

x=2

on the interval

[0,4]

. Assume

r(x)>s(x)

for

0\le x<2

and

r(x)<s(x)

for

2<x\le4

. Which of the following integrals equals the area of the region enclosed by the graphs of

r

and

s

between

x=0

and

x=4

? (a)

\displaystyle \int_{0}^{2}\bigl(s(x)-r(x)\bigr)\,dx+\int_{2}^{4}\bigl(r(x)-s(x)\bigr)\,dx

(b)

\displaystyle \int_{0}^{2}\bigl(r(x)-s(x)\bigr)\,dx+\int_{2}^{4}\bigl(s(x)-r(x)\bigr)\,dx

(c)

\displaystyle \int_{0}^{4}\bigl(r(x)-s(x)\bigr)\,dx

(d)

\displaystyle \int_{0}^{2}\bigl(r(x)-s(x)\bigr)\,dx-\int_{2}^{4}\bigl(r(x)-s(x)\bigr)\,dx