Integrals Test ...

If $$\displaystyle  I =\int_{0}^{a} \sqrt {\frac{a-x}{a+x}}dx, a > 0,$$ then $$I$$ equals

Value of $$\displaystyle \int_{0}^{\pi /2}\displaystyle \frac{\sin 4\Theta }{\sin \Theta }\: d\Theta $$ is

If $$ \displaystyle I = \int_{0}^{\pi/2} \frac{dx}{5+3\sin x}  =\lambda \tan^{-1} \left(\frac{1}{2}\right ) $$ then
value of $$\lambda $$ is

 If $$\displaystyle I = \int_{1/3}^{3}\frac{1}{x}\sin \left (\frac{1}{x}-x \right) dx,$$ then $$I$$ equals

 If $$\displaystyle I=\int _{8}^{15} \frac{dx}{(x-3)\sqrt{x+1} }$$ then$$ I$$ equals

37 If $$ n > 1,$$ and $$ \displaystyle I=\int _{0}^{\infty} \frac{dx}{(x+\sqrt{1+x^{2}})^{n}}$$ then $$ I$$  equals

 If $$\displaystyle I = \int _{0}^{1} \frac{dx}{(1+ x)(2 + x)\sqrt{x(1-x)}}$$ then $$I$$ equals

If $$ h(x) = \int _{1}^{x} \sin^{4} t dt,$$ then $$ h(x + \pi)$$ equals

 If $$\displaystyle \int _{0}^{1}\frac{\sin t}{1+t} dt = \alpha$$. then value of
$$\displaystyle I=\int_{4\pi-2}^{4\pi}\frac{\sin(x/2)}{4\pi+2-x} dx $$

 If $$\displaystyle I = \int_{0}^{\pi/4}  \frac{ \sin 2\theta }{ \sin^{2} \theta +\cos ^{4} \theta } d \theta $$