Question

test for convergence

Answer 1

How can I check the convergence of
\[\int\limits_{0}^{\pi} \frac{\sin(x)}{\sqrt{\pi-x}}dx\]
Applying the property
\[\int\limits_{0}^{a}f(x)dx=\int\limits_{0}^{a}f(a-x)dx\]
\[\int\limits_{0}^{\pi}\frac{\sin(x)}{\sqrt{x}}dx\]
After that I'm stuck

Answer 2

@IrishBoy123 @ganeshie8

Answer 3

@Hero

Answer 4

you just want the test for the convergence, right ?

Answer 5

since \(0\le \sin x \le 1\) over the given interval, you may use below for comparison :
\[\dfrac{\sin x}{\sqrt{x}} \le \dfrac{1}{\sqrt{x}}\]

Answer 6

oh, ok thanks!!