Suppose $f$ is such that $f\,\,\left( { - x} \right) = - \,f\,\left( x \right)$ for every real $x$ and $\mathop \smallint \nolimits_0^1 \,\,f\left( x \right)\,\,dx = 5$, then $\mathop \smallint \nolimits_{ - 1}^0 \,\,\,\,f\left( t \right)\,\,dt$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

Suppose

f

is such that

f\,\,\left( { - x} \right) = - \,f\,\left( x \right)

for every real

x

and

\int \nolimits_0^1 \,\,f\left( x \right)\,\,dx = 5

, then

\int \nolimits_{ - 1}^0 \,\,\,\,f\left( t \right)\,\,dt

is equal to

View answer and explanation

Correct option: D

- \,5

Option D (-5) is correct because f(x) is an odd function, and the integral from -1 to 0 is the negative of the integral from 0 to 1.

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