Mathematics

Problem

f(x) \ge 0, \forall x \in (0, 2)

and

y = f(x)

makes positive intercepts of 2 and 1 unit on

X

and

Y

-axes respectively and encloses an area of

3/4

unit with axes, then

\int_{0}^{2} xf'(x) dx

is a.

\frac{3}{4}

b. 1 c.

\frac{5}{4}

-\frac{3}{4}