Let ( and is an integer)

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

Let

I_n = \int_{0}^{\pi/4} \tan^n x \, dx

(

n > 1

and is an integer). Show that (i)

I_n + I_{n-2} = \frac{1}{n-1}

(ii)

\frac{1}{2(n+1)} < I_n < \frac{1}{2(n-1)}