The value of int_0^{pi /2} frac{dx}{1 + tan^3 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $I = \int_0^{\pi /2} \frac{dx}{1 + 	an^3 x}$.Using the property $\int_0^a f(x) dx = \int_0^a f(a-x) dx$,we have:$I = \int_0^{\pi /2} \frac{dx

Vedclass · Accepted Answer

$\frac{\pi}{4}$

Vedclass · Answer

(D) Let $I = \int_0^{\pi /2} \frac{dx}{1 + 	an^3 x}$.Using the property $\int_0^a f(x) dx = \int_0^a f(a-x) dx$,we have:$I = \int_0^{\pi /2} \frac{dx}{1 + 	an^3(\pi/2 - x)} = \int_0^{\pi /2} \frac{dx}{1 + \cot^3 x}$.$I = \int_0^{\pi /2} \frac{	an^3 x}{1 + 	an^3 x} dx$.Adding the two expressions for $I$:$2I = \int_0^{\pi /2} \left( \frac{1}{1 + 	an^3 x} + \frac{	an^3 x}{1 + 	an^3 x} ight) dx$.$2I = \int_0^{\pi /2} \frac{1 + 	an^3 x}{1 + 	an^3 x} dx = \int_0^{\pi /2} 1 dx$.$2I = [x]_0^{\pi /2} = \frac{\pi}{2}$.Therefore,$I = \frac{\pi}{4}$.

The value of $\int_0^{\pi /2} \frac{dx}{1 + \tan^3 x}$ is

Similar Questions

$\int_0^{\infty} (x^{12} + x^{-12}) \frac{\log x}{x} dx =$

If $I_n = \int_0^{\pi / 2} \sin^n(x) dx$ and $I_n = (k) I_{n-2}$,then what will be the value of $k$?

Let $N$ be the set of natural numbers. For $n \in N$,define $I_n = \int_0^\pi \frac{x \sin^{2n}(x)}{\sin^{2n}(x) + \cos^{2n}(x)} dx$. Then,for $m, n \in N$,which of the following is true?

Evaluate the definite integral: $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{d x}{1+\sqrt{\cot x}}$.

$\int_{-1}^{1} \sin^3 x \cos^2 x \, dx = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module