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

  • Option 1)

    18

  • Option 2)

    20

  • Option 3)

    40

  • Option 4)

    None

 

Answers (1)

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

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