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prove that int[ from (0) to(2pi) ][1 / 1+3(cos x)^2]dx = pi

   prove that


   int[ from (0) to(2pi) ][1 / 1+3(cos x)^2]dx = pi

Grade:12

1 Answers

gOlU g3n|[0]uS
42 Points
10 years ago

ans-   baha  put    3(cos2 x )=3[(1+cos2x)/2]

                                       =3/2(1+cos2x) = 3/2 + 3/2cos2x.

        THEN   cos2x = (1 - tan2 x) / (1+tan2 x).

        [ (1 + tan2 x)dx/[5/2(1+tan2 x) + 3/2(1 - tan2 x)] ]

        2[ sec2 x dx/ ( 5 +5tan2 x + 3 - 3tan2 x)

        2[ sec2 x dx / ( 8+ 2tan2 x)]

         [ sec2 x dx/ (4 + tan2 x)]            THEN let tanx = t => sec2 x dx = dt

        [ dt/(4+ t2 )] integrate ur ans will com

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