If for all and makes positive intercepts of units and unit on the - and -axes

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

f(x)\ge0

for all

x\in(0,2)

and

y=f(x)

makes positive intercepts of

2

units and

1

unit on the

x

- and

y

-axes, respectively, and encloses an area of

\frac34

square unit with the axes, then

\int_0^2xf'(x)\,dx

is (1)

\frac34

(2)

1

(3)

\frac54

(4)

-\frac34