If $k\,\mathop \smallint \nolimits_0^1 \,\,x\,.\,f\left( {3x} \right)dx = \mathop \smallint \nolimits_0^3 \,t\,.\,f\,\,\left( t \right)\,\,dt$ then the value of $k$ is

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

k\,\int \nolimits_0^1 \,\,x\,.\,f\left( {3x} \right)dx = \int \nolimits_0^3 \,t\,.\,f\,\,\left( t \right)\,\,dt

then the value of

k

View answer and explanation

Correct option: A

Option A (9) is correct because by substituting

t = 3x

, the integral transforms, and solving for

k

yields 9.

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