If $\mathop \smallint \nolimits_a^b \,\,{x^3}\,\,\;dx = 0$ and if $\mathop \smallint \nolimits_a^b \,\,{x^2}\;\,dx = \frac{2}{3}$, then the values of $a\;\,\,{\rm{and}}\,\,\;b$ are respectively

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \nolimits_a^b \,\,{x^3}\,\,\;dx = 0

and if

\int \nolimits_a^b \,\,{x^2}\;\,dx = \frac{2}{3}

, then the values of

a\;\,\,\mathrm{and}\,\,\;b

are respectively

View answer and explanation

Correct option: D

- 1,\,\,1

Option D (

- 1,\\,\\,1

) is correct because the integral of an odd function from -a to a is 0, and the integral of x² from -1 to 1 is 2/3.

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