The value of \int_{-\pi \/ 3}^{\pi \/ 3} \frac{x \sin x}{\cos ^2 x} \dx is:

Correct Answer is : 4π3−2logtan(5π12)

\frac{4 \pi}{3}-2 \log \tan (\frac{5 \pi}{12})

\frac{4 \pi}{3}+\log \tan (\frac{5 \pi}{12})

\frac{4 \pi}{3}-\log \tan (\frac{5 \pi}{3})

NIMCET 2023 Question Paper with solutions

Question : 3 of 120

Marks: +1, -0

The value of

∫↙{-π \/ 3}↖{π \/ 3} \;{x sin \;x}/{\cos ^2 x} \dx

is:

Solution:

(B):

{\I}=2 ∫↙{0}↖{π \/ 3} x \tan x \ sec x \dx

Using Integration by parts

{\I}=2[x \ sec x]_0^{π \/ 3}-2 ∫↙{0}↖{π \/ 3} \ sec x \dx

\;=2 [\;{π}/{3} × 2] -2[\ln |\ sec x+\tan x|]_0^{π \/ 3}

\;=\;{4 π}/{3}-[\ln |2+{√{3}}|]=\;{4 π}/{3}-2 \ln \tan \;{5 π}/{12} .

Go to Question:

Prev Question

Next Question