The value of the integral \int_{0}^{\pi} x \cos ^{2} x d x is

GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 63 of 65

Marks: +1, -0

The value of the integral

∫↙{0}↖{π} x \cos ^{2} x d x

Solution:

The value of

∫↙{0}↖{π} x \cos ^{2} x d x

=∫↙{0}↖{π}(\;{x}/{2}+\;{x \cos 2 x}/{2}) d x

=\;{x^{2}}/{4}|_{0} ^{π}+\;{1}/{2}(\;{x \sin 2 x}/{2}+\;{\cos 2 x}/{4})

=\;{π^{2}}/{4}+\;{1}/{2}\{(0+\;{1}/{4})-(0+\;{1}/{4})\}

=\;{π^{2}}/{4}+\;{1}/{2}(\;{1}/{4}-\;{1}/{4})

=\;{π^{2}}/{4}

Go to Question:

Prev Question

Next Question