6 0 | ( sin 3 x + sin 2 x + sin x ) | ? d x is equal to_____. [2026]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
$6 \int_{0}^{π}$ $| (\sin 3 x + \sin 2 x + \sin x) |$ $d x$ is equal to_____. [2026]

Ans.
(17)

$6 \int_{0}^{π}$ $| 2 \sin 2 x \cos x + \sin 2 x |$ $d x$

$= 6 \int_{0}^{π}$ $| 4 \sin x \cos^{2} x + 2 \sin x \cos x |$ $d x$

$I = 12 \int_{0}^{π}$ $| \sin x (2 \cos^{2} x + \cos x) |$ $d x$

Put $\cos x = t, - \sin x d x = d t$

$I = - 12 \int_{1}^{- 1}$ $| 2 t^{2} + t |$ $d t$

$I = 12 (\int_{- 1}^{- \frac{1}{2}} (2 t^{2} + t) d t + \int_{- \frac{1}{2}}^{0} - (2 t^{2} + t) d t + \int_{0}^{1} (2 t^{2} + t) d t)$

$I = 17$

Want Us to Email you About Special Offers & Updates?