The value of the integral \int^{\pi}_{0}(1-|\sin8x|)dx is

KVPY SX SB Exam 2018 Question Paper

Question : 12 of 120

Marks: +1, -0

The value of the integral

∫↖{π}↙{0}(1-|\sin8x|)dx

Solution:

∫↖{π}↙{0}(1-|\sin8x|)dx

=π-8∫↖{π/8}↙{0}( \sin8x)dx

(∵ |sin 8x| is periodic with period

π/8

)
= π – 2

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