31 votes 31 votes If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______. Calculus gatecse-2014-set3 calculus integration limits numerical-answers easy + – go_editor asked Sep 28, 2014 go_editor 10.8k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Split in two intervals: 0 to π and π to 2kπ as sin x is negative in π to 2π. Then use Integration By Parts with ILATE sequence. Answer is: 4 Dhananjay answered Jan 22, 2015 Dhananjay comment Share Follow See all 21 Comments See all 21 21 Comments reply eppshankar asked Feb 3, 2015 Is the integral of second half i.e [π , 2π] being subtracted from that of the first[0, π] ? Is it right to do so? Krithiga2101 commented Jan 4, 2018 reply Follow Share We can use the property of definite integral and apply the formula for limits and solve instead of byparts method too 0 votes 0 votes Please log in or register to add a comment.