int_0^{pi /2} frac{dx}{1 + tan^3 x} का मान है | vedclass

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

Question

(D) माना $I = \int_0^{\pi /2} \frac{dx}{1 + 	an^3 x}$.गुणधर्म $\int_0^a f(x) dx = \int_0^a f(a-x) dx$ का उपयोग करने पर:$I = \int_0^{\pi /2} \frac{dx}

Vedclass · Accepted Answer

$\frac{\pi}{4}$

Vedclass · Answer

(D) माना $I = \int_0^{\pi /2} \frac{dx}{1 + 	an^3 x}$.गुणधर्म $\int_0^a f(x) dx = \int_0^a f(a-x) dx$ का उपयोग करने पर:$I = \int_0^{\pi /2} \frac{dx}{1 + 	an^3(\pi/2 - x)} = \int_0^{\pi /2} \frac{dx}{1 + \cot^3 x}$.$I = \int_0^{\pi /2} \frac{	an^3 x}{1 + 	an^3 x} dx$.$I$ के दोनों समीकरणों को जोड़ने पर:$2I = \int_0^{\pi /2} \left( \frac{1}{1 + 	an^3 x} + \frac{	an^3 x}{1 + 	an^3 x} ight) dx$.$2I = \int_0^{\pi /2} \frac{1 + 	an^3 x}{1 + 	an^3 x} dx = \int_0^{\pi /2} 1 dx$.$2I = [x]_0^{\pi /2} = \frac{\pi}{2}$.अतः,$I = \frac{\pi}{4}$.

$\int_0^{\pi /2} \frac{dx}{1 + \tan^3 x}$ का मान है

Similar Questions

$\int\limits_0^\infty {\frac{{{x^3}}}{{1 + x + 2{x^2} + 2{x^3} + {x^4} + {x^5}}}} dx$

$\int_0^{\frac{\pi}{4}} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x=$

$\int_{-5}^{5} \log \left(\frac{7-x}{7+x}\right) dx =$

$\int\limits_{ - \pi /2}^{\pi /2} {\frac{{{{\sin }^2}x}}{{1 + {2^x}}}dx} $ का मान क्या है?

$\int_0^{\frac{\pi}{4}} \log \left(\frac{\sin x+\cos x}{\cos x}\right) d x=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module