Let be continuous on and define

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Let

h

be continuous on

[0,5]

and define

H(x)=\displaystyle\int_{0}^{x} h(t)\,dt

. Suppose

h(t)>0

for

0<t<2

and

h(t)<0

for

2<t<5

. Which of the following is TRUE about

H

on the interval

(0,5)

? (a)

H

is decreasing on

(0,2)

and increasing on

(2,5)

. (b)

H

is increasing on

(0,5)

. (c)

H

is increasing on

(0,2)

and decreasing on

(2,5)

. (d)

H

is increasing on

(0,3)

and decreasing on

(3,5)

.

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