Question

Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.

Options

• 6.00

• 7.00

• 8.00

• 9.00

Answer 1

Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to 8.00.

Explanation:

I = `int_0^∞ (t^4dt)/(1 + t^2)^6`

Let t = tanθ

dt = sec²θdθ

= `int_0^(π/2)(tan^4θsec^2θdθ)/(sec^12θ)`

= `int_0^(π/2)sin^4θ.cos^6θdθ`

= `((3.1).(5.3.1))/((10.8.6.4.2)).π/2`

= `(3π)/512`

⇒ k = 8