For a continuous rate function on

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For a continuous rate function

r

[a,b]

, which of the following conditions is sufficient to guarantee that

\displaystyle \int_{a}^{b} r(x)\,dx = \int_{a}^{b} |r(x)|\,dx

? (a)

r(x)\le 0

for all

x

[a,b]

(b)

\displaystyle\int_{a}^{b} r(x)\,dx = 0

(c)

r(x)\ge 0

for all

x

[a,b]

(d)

r(x)

attains both positive and negative values on

[a,b]