If $\mathop \smallint \limits_a^b \,\,\frac{{{x^n}}}{{{x^n} + \,\,{{\left( {16 - x} \right)}^n}}}\,\,dx = 6$, then

$a = - \,4,\,\,b = 20,\,\,n \in R$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Medium

1 of 1

Analyzing +4 | -1

\int \limits_a^b \,\,\frac{{{x^n}}}{{{x^n} + \,\,{{\left( {16 - x} \right)}^n}}}\,\,dx = 6

, then

View answer and explanation

Correct option: B

a = 2,\,\,b = 14,\,\,n \in R

Option B (

a = 2,\,b = 14,\,n \in R

) is correct because it satisfies the property of definite integrals where the integral's value depends on the limits of integration, and

a+b = 16

and

\frac{b-a}{2} = 6

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)