Let be continuous on with for and

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

Let

h

be continuous on

[0,8]

with

h(x)\ge 0

for

0\le x\le 2

and

6\le x\le 8

, while

h(x)\le 0

for

2\le x\le 6

. Given that

\displaystyle\int_{0}^{8} h(x)\,dx=-3

and

\left|\int_{6}^{8} h(x)\,dx\right|=1

, identify which integral has the greater absolute value:

\displaystyle\int_{0}^{2} h(x)\,dx

\displaystyle\int_{2}^{6} h(x)\,dx