QJEEM02Ma6dea: JEE Main 2002 Mathematics - Class 12 JEEM02Ma6dea Solution: If y = f ( x ) makes + v e intercept of 2 and 0 unit on x and y …

Question

Verified Solution • 2025–26 Session moderate

If

y = f (x)

makes +

v e

intercept of

2

and

0

unit on

x

and

y

axes and encloses an area of

3 / 4

square unit with the axes then

\int_{0}^{2} x f^{'} (x) d x

is

Accepted Answer

We have

\int_{0}^{2} f (x) d x = \frac{3}{4}; N o w,

\int_{0}^{2} x f^{'} (x) d x

= x \int_{0}^{2} f^{'} (x) d x - \int_{0}^{2} f (x) d x

= {[x f (x)]}_{0}^{2} - \frac{3}{4}

= 2 f (2) - \frac{3}{4}

= 0 - \frac{3}{4}

(

As

f (2) = 0

)

= - \frac{3}{4} .

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