JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

{b_n} = \int_0^{\frac{\pi }{2}} {\frac{{{{\cos }^2}nx}}{{\sin x}}} \,\,dx,\,\,\,\,n \in \mathbb{N},

then,

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Correct option: D

\frac{1}{{{b_3} - {b_2}}},\frac{1}{{{b_4} - {b_3}}},\frac{1}{{{b_5} - {b_4}}}

are in an A.P. with common difference –2

Option D (

\frac{1}{{{b_3} - {b_2}}},\frac{1}{{{b_4} - {b_3}}},\frac{1}{{{b_5} - {b_4}}}

are in an A.P. with common difference –2) is correct because by evaluating the integral and finding the differences between consecutive terms, we can show that the reciprocals form an arithmetic progression.

More Questions from DEFINITE INTEGRATION

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

is equal to If

f\left( x \right)

is differentiable and

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

, then

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

equals The value of

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

, where

[*]

denotes the greatest integer function, is The integral

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

is equal to: The definite integral

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

equals If

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

,then the expression for

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

in terms of

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