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\int_{\pi}^{10\pi}\left | sinx \right |dx=

  • Option 1)

    18

  • Option 2)

    20

  • Option 3)

    40

  • Option 4)

    None

 

Answers (1)

best_answer

As 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.

 

 

\int_{\pi }^{10\pi }\left | \sin \right |dx \: \: \: \Rightarrow \sin x=0 \: \: at \: \: x=n\pi

and

There are 9 loops which each having value 2.

\therefore 2\times 9=18

 

\\ -\int_{\pi }^{2\pi }\sin xdx \: \: = \: -(-\cos x) \int_{\pi }^{2\pi} \\

                          \\ =\cos 2\pi -\cos \pi \\ =1-(-1)=2  because from \pi \: to \: 2\pi \:\sin x is negative


Option 1)

18

This option is correct

Option 2)

20

This option is incorrect

Option 3)

40

This option is incorrect

Option 4)

None

This option is incorrect

Posted by

divya.saini

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