JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f(\theta)=\frac{4}{3}\left(1-\cos ^6 \theta-\sin ^6 \theta\right)

, then

\lim \limits_{{n \rightarrow \infty}} \frac{1}{n}\left[\sqrt{f\left(\frac{1}{n}\right)}+\sqrt{f\left(\frac{2}{n}\right)}+\sqrt{f\left(\frac{3}{n}\right)}+\ldots+\sqrt{f\left(\frac{n}{n}\right)}\right]=

View answer and explanation

Correct option: D

\frac{1-\cos 2}{2}

Option D (

\frac{{1-\cos 2}}{{2}}

) is correct because the limit can be expressed as a definite integral, which simplifies to

\int_0^1 \sin 2x dx

, and evaluating this integral yields

\frac{{1-\cos 2}}{{2}}

More Questions from DEFINITE INTEGRATION

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[*]

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