Prove that \int_{0}^{ {\a}} {\f}(x) {\d} x=\int_{0}^{ {\a}} {\f}( {\a}-x) {\d} x, hence evaluate \int_{0}^{\pi} \frac{x \sin x}{1+\cos ^2 x} {\d} x.

CBSE Class 12 Math 2019 Delhi Set 1 Solved Paper - Question 20

Question : 20 of 29

Marks: +1, -0

Prove that

∫↙{0}↖{ {\a}} {\f}(x) {\d} x=∫↙{0}↖{ {\a}} {\f}( {\a}-x) {\d} x

, hence evaluate

∫↙{0}↖{π} \;{x sin \;x}/{1+\cos ^2 x} {\d} x

Solution:

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