JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Medium

1 of 1

Understanding +4 | -1

Let

f(x)

be a continuous function defined on

[0, a]

such that

f(a-x)=f(x)

for all

x \in[0, a]

. If

\int_0^{a / 2} f(x) d x=\alpha

, then

\int_0^a f(x) d x

is equal to

View answer and explanation

Correct option: B

2 \alpha

Option B (

2 \alpha

) is correct because using the property

\int_0^a f(x) dx = \int_0^{a/2} [f(x) + f(a-x)] dx

and the given condition

f(a-x)=f(x)

, we get

\int_0^a f(x) dx = 2 \int_0^{a/2} f(x) dx = 2\alpha

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)