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  • I have a doubt, kindly clarify. - Integral Calculus - JEE Main

\int_{\pi }^{10\pi }\left | sin\, x \right |dx\; is

  • Option 1)

    20

  • Option 2)

    8

  • Option 3)

    10

  • Option 4)

    18.

 

Answers (1)

best_answer

As learnt in concept

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.

 

 \int_{\pi}^{10\pi}\left | sin\ x \right | dx=9\int_{0}^{\pi}\left | sin\ x \right | dx

=>9[-cosx]_{0}^{\pi}=9[1+1]=18


Option 1)

20

This is incorrect

Option 2)

8

This is incorrect

Option 3)

10

This is incorrect

Option 4)

18.

This is correct

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perimeter

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