Let for all in

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

Problem

Let

f(x)\le 0

for all

x

[p,q]

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

y=f(x)

, the

x

-axis, and the lines

x=p

and

x=q

? (a)

\displaystyle \int_q^p f(x)\,dx

(b)

\displaystyle \dfrac12\int_p^q f(x)\,dx

(c)

\displaystyle \int_p^q \bigl(-f(x)\bigr)\,dx

(d)

\displaystyle \int_p^q f(x)\,dx