COMEDK 2024 Shift 2 Paper

If In=

‌ π 4

∫

0

tannx‌dx, for n≥2, then In+In−2=
We can solve this problem using integration by parts. Let's start by writing out the integral for In :
We can then use the identity tan2x=sec2x−1 to rewrite the integral as:
Let's focus on the first integral. We can use u-substitution with u=tan‌x and du=sec2x‌dx :
The second integral is simply In−2. Therefore, we can write:
In=‌

1

n−1

−In−2
Rearranging this equation, we get:
In+In−2=‌

1

n−1

So the answer is Option A.