Let f(x) be a non negative continuous function such that the area bounded by the curve y=f(x),x axis and the ordinates x=pi/4 , x=Beta pi/4 is.... then f(pi/2)=?

Question

Let f(x) be a non negative continuous function such that the area bounded by the curve y=f(x),x axis and the ordinates x=pi/4 , x=Beta >pi/4 is.... then f(pi/2)=?

dls · Answer

$$\LARGE Area= (\beta \sin \beta+\frac{\pi}{4} \cos \beta+\sqrt(2)\beta)$$

dls · Answer

@ganeshie8

dls · Answer

$$\LARGE \int\limits_\frac{\pi}{4}^\beta f(x)dx=\LARGE  (\beta \sin \beta+\frac{\pi}{4} \cos \beta+\sqrt(2)\beta)$$
seems so..

ganeshie8 · Answer

try differentiating $A(\beta)$,   to get $f(\beta)$
then sub $\beta = \pi/2$

dls · Answer

how? isnt Beta a constant so itll be 0

ganeshie8 · Answer

$\beta$ varies from pi/4 to infinity

ganeshie8 · Answer

int  pi/4 to $\beta$

is same as

int 0 to $x$

if we shift the origin, right ?

ganeshie8 · Answer

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