A continuous function on satisfies the following conditions

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

A continuous function

p

[-4,6]

satisfies the following conditions. •

p(x) > 0

(-4,-1)

and the area enclosed between the curve

y=p(x)

, the

x

-axis and the lines

x=-4

and

x=-1

9

square units. •

p(x) < 0

(-1,3)

and the area enclosed between the curve, the

x

-axis and the lines

x=-1

and

x=3

5

square units. •

p(x) > 0

(3,6)

and the area enclosed between the curve, the

x

-axis and the lines

x=3

and

x=6

4

square units. Answer the following: (i) Find the value of

\displaystyle \int_{-4}^{6} p(x)\,dx

. (ii) Using the given information, determine

\displaystyle \int_{3}^{6} p(x)\,dx

. (iii) Compare the magnitudes

\bigl|\displaystyle \int_{-4}^{-1} p(x)\,dx\bigr|

and

\bigl|\displaystyle \int_{-1}^{3} p(x)\,dx\bigr|

and state which is larger. Give a reason for your answer.