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  • How to solve this problem- - Integral Calculus - JEE Main-3

\int_{0}^{4\Pi }\left | \cos x \right |dx

  • Option 1)

    4

  • Option 2)

    6

  • Option 3)

    8

  • Option 4)

    10

 

Answers (1)

best_answer

As we learnt

Properties of Definite Integration -

For periodic function

Let Period (T) then

\int_{0}^{nT}f(n)dx= n\int_{0}^{T}f(x)dx

 

- wherein

Where f(x) is periodic function with period T and n is any integer.

 

 Note that |cos x| is a periodic function with period p. Hence the given integral

I=4\int_{0}^{\pi}\left | \cos x \right |dx

    =4\left [ \int_{0}^{\pi/2}\cos x \, dx - \int_{\pi/2}^{\pi}\cos x \, dx\right ]=4\left [ \left [ \sin x \right ]_{0}^{\pi/2} -\left [ \sin x \right ]_{\pi/2}^{\pi}\right ]=4\left [ 1+1 \right ]=8


Option 1)

4

Option 2)

6

Option 3)

8

Option 4)

10

Posted by

gaurav

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