If-f-3-3-f-1-2-1-3-f-x-f-x-dx-

Question Number 38405 by malwaan last updated on 25/Jun/18

If f (3) = 3; f (1) = 2

\Rightarrow \int_{1}^{3} f (x) f^{^{'}} (x) dx = \dots . .

Commented by tanmay.chaudhury50@gmail.com last updated on 25/Jun/18

p l s c l a r i f y [(x)] i s i t f l o o r / g r e a t e s t i n t e g e r

f u n c t i o n

Commented by malwaan last updated on 25/Jun/18

I am sorry

It is f (x)

Answered by tanmay.chaudhury50@gmail.com last updated on 25/Jun/18

\int_{1}^{3} f (x) \times \frac{d f (x)}{d x} d x

\int_{1}^{3} f (x) d f (x)

∣ \frac{{f (x)}^{2}}{2} ∣_{1}^{3}

= \frac{1}{2} {f (3) \times f (3) - f (1) \times f (1)}

\frac{1}{2} (3^{2} - 2^{2}) = \frac{5}{2}