JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

Let

a

and

b

be real constants such that the function

f

defined by

f(x)=\left\{\begin{array}{cc}x^2+3 x+a, & x \leq 1 \\ b x+2, & x > 1\end{array}\right.

be differentiable on

\mathbb{R}.

Then, the value of

\int\limits_{{-2}}^2 f(x) d x

equals

View answer and explanation

Correct option: B

The correct answer is B (17) because by ensuring differentiability and continuity, we can find the values of a and b, and then evaluate the definite integral.

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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)