Tiny integral

Calculus Level 3

$\large \int_{-1}^0 \sqrt{\frac{1+x}{1-x}} \, dx$

If the value of the integral above equals to $\frac AB (\pi - B)$ for positive integers $A$ and $B$ , find the value of $A+B$ .

1 solution

Tanishq Varshney
Sep 4, 2015

Let $1-x=t^2$ then proceed to simple integration of

$\large {\displaystyle 2 \int^{\sqrt{2}}_{1} \sqrt{2-t^2} dt}$

The final answer is $\large{\frac{1}{2}(\pi-2)}$

Nice solution but is there any way to know what are we supposed to substitute since we got a lot of options ?

Syed Baqir - 5 years, 9 months ago

Or u can put $x=\cos 2y$

Tanishq Varshney - 5 years, 9 months ago

How did you get the limits as (1.414) & [1]..?Please explain?

Yuki Kuriyama - 5 years, 9 months ago

That is because of substitution !!

1 - 0 =t^{2} => t = 1

1- (-1) = t^{2} => \sqrt{2}

Syed Baqir - 5 years, 9 months ago

Ohh..gr8 thanx a lot !..:)

Yuki Kuriyama - 5 years, 9 months ago

@Yuki Kuriyama – no problem, I am glad it helped . :D

Syed Baqir - 5 years, 9 months ago