If $\mathop \smallint \nolimits_0^a \,\,f\left( {2a - x} \right)dx = {\rm{\mu \;\;}}\,\,{\rm{and}}\,\,\mathop \smallint \nolimits_0^a \,\,f\left( x \right)\;dx = \lambda $, then $\mathop \smallint \nolimits_0^{2a} \,\,f\left( x \right)\,dx$ equals

$\lambda \,\, + \,\,{\rm{\mu }}$

$2\,\lambda \,\, - \,\,{\rm{\mu }}$

${\rm{\mu }}\,\, - \,\,\lambda $

$\lambda \,\, - \,\,2{\rm{\mu }}$

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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

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

, then

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

equals

View answer and explanation

Correct option: B

\lambda \,\, + \,\,\mathrm{\mu }

Option B is correct because the integral from 0 to 2a can be split into two integrals, each from 0 to a, and then using the given information, the result is

\lambda + \mu

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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