The value of the integral ∫ 0 π 1 - | sin 8 x | d x is

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

The value of the integral

\int_{0}^{π} (1 - | \sin 8 x |) d x

is

MathematicsDefinite IntegrationKVPYKVPY 2018 (SB/SX)

Options:

A $0$
B $π - 1$
C $π - 2$
D $π - 3$

Solution:

2163 Upvotes Verified Answer

The correct answer is:

π - 2

Let $I = \int_{0}^{π} (1 - | \sin 8 x |) d x$

$I = \int_{0}^{π} d x - \int_{0}^{π} | \sin 8 x | d x$

$I = π - \int_{0}^{\frac{π}{8} \times 8} | \sin 8 x | d x$

$I = π - 8 \int_{0}^{\frac{π}{8}} \sin 8 x d x$ [ $∵ \sin 8 x B$ periodic with $\frac{π}{8}$ ]

$I = π - 8 {[\frac{- \cos 8 x}{8}]}_{0}^{π / 8}$

$I = π + (\cos π - \cos 0) = π - 2$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play