JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Hard

1 of 1

Application +4 | -1

\int \limits_{ - \pi }^\pi \,\,{\left[ {\cos \,\,px\,\, - \,\,\sin \,\,qx} \right]^2}dx

, where

p,\;\,q

are integers is equal to

View answer and explanation

Correct option: D

2\,\pi

Option D (

2\pi

) is correct because when integrating the square of

(\cos px - \sin qx)

from

-\pi

\pi

, the cross term vanishes due to symmetry, and the integrals of

\cos^2 px

and

\sin^2 qx

each contribute

\pi

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