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Thread: kindly explain me solution of integration

  1. #1
    Member moonnightingale's Avatar
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    kindly explain me solution of integration

    Kindly explain me this solution in detail
    I have attached the three questions. I will be highly greatful if anyone of you explain me these solutions in Detail. Thaks a lot

    kindly explain me solution of integration-question-1.jpg

    kindly explain me solution of integration-question-2.jpg
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by moonnightingale View Post
    Kindly explain me this solution in detail
    I have attached the three questions. I will be highly greatful if anyone of you explain me these solutions in Detail. Thaks a lot

    Click image for larger version. 

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    $\displaystyle \cos^2(2 \pi f_0 t) = (\cos(4 \pi f_0 t)+1)/2$

    then as $\displaystyle \cos$ is symetrical in all sorts of ways the right hand side will integrate up to half the area eonclosed in the rectangle enclosing the curve, which has height $\displaystyle 1$ and length $\displaystyle T_0$.

    (Draw a picture of the curve, it will then be obvious)

    CB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by moonnightingale View Post
    Kindly explain me this solution in detail
    I have attached the three questions. I will be highly greatful if anyone of you explain me these solutions in Detail. Thaks a lot

    Click image for larger version. 

Name:	question 1.JPG 
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ID:	12939

    Click image for larger version. 

Name:	question 2.JPG 
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    (b) is a direct consequence of (a) (multiply the integral in (a) by $\displaystyle T_0$ to get that in (b)

    CB
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