If $\mathop \smallint \nolimits_0^a \,\,f\left( {2a\,\, - \,\,x} \right)\,\,dx = m\;\,\,{\rm{and}}\,\,\mathop \smallint \nolimits_0^a \,\,f\left( x \right)dx = n$, then $\mathop \smallint \nolimits_0^{2a} \,\,f\left( x \right)\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \nolimits_0^a \,\,f\left( {2a\,\, - \,\,x} \right)\,\,dx = m\;\,\,\mathrm{and}\,\,\int \nolimits_0^a \,\,f\left( x \right)dx = n

, then

\int \nolimits_0^{2a} \,\,f\left( x \right)\,\,dx

is equal to

View answer and explanation

Correct option: D

m\,\, + \,\,n

Option D (

m\\ + \\ n

) is correct because

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

can be split into two integrals, and using the given information, it equals

m\\ + \\ n

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