JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Medium

1 of 1

Application +4 | -1

Given that

\int \frac{d x}{\left(1+x^2\right)^n}=\frac{x}{2(n-1)\left(1+x^2\right)^{n-1}}+\frac{(2 n-3)}{2(n-1)} \int \frac{d x}{\left(1+x^2\right)^{n-1}}

. Find the value of

\int\limits_{0}^1 \frac{d x}{\left(1+x^2\right)^4}

:
(you may or may not use reduction formula given)

View answer and explanation

Correct option: A

\frac{11}{48}+\frac{5 \pi}{64}

Option D (

\frac{\pi}{4}

) is correct because using the property

\int_a^b f(x) dx = \int_a^b f(a+b-x) dx

, the integral simplifies to

\int_0^{\pi/2} \cos^2 x dx = \frac{\pi}{4}

More Questions from DEFINITE INTEGRATION

Practice All Chapter MCQs →

\int \nolimits_0^\infty \,\,\log \,\,\left( {x + \frac{1}{x}} \right)\,\,\frac{{dx}}{{1 + {x^2}}}

f\left( x \right)

\int \nolimits_0^{{t^2}} \,\,x\;\,f\left( x \right)\,\,dx = \frac{2}{5}\,\,{t^5}

f\left( {\frac{4}{{25}}} \right)

\int\limits_{{0}}^{11}[x]^{3} . \mathrm{dx}

[*]

\int\limits_{2}^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} d x

\int\limits_{{-2}}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x

I\,\,\left( {m,\,\,n} \right) = \int \nolimits_0^1 \,\,{t^m}\,\,{\left( {1 + t} \right)^n}\,\,dt

I\left( {m,\,\,n} \right)

I\,\,\left( {m + 1,\,\,n + 1} \right)