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bii17

  • 2 years ago

integrate (x-x^2) / sqrt (1-x^2)

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  1. TheRealMeeeee
    • 2 years ago
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    ok Hemant answered 4 years ago Standard Formula : ∫ [ 1 / √( a² - u² ) ] du = arcsin ( u / a ) ........... (1) ......................................... I = ∫ [ 1 / √( x - x² ) ] dx ............. (2) ......................................... We have √( x - x² ) = √[ - ( x² - x ) ] = √[ (1/4) - ( x² - x + 1/4 ) ] = √[ (1/2)² - ( x- 1/2 )² ] ..... (3) ......................................... From (2) and (3), then, I = ∫ { 1 / √[ (1/2)² - ( x- 1/2 )² ] } dx ..= ∫ { 1 / √[ (1/2)² - u² ] } du, ............ where ... u = x - 1/2 ..= arcsin [ u / (1/2) ] + C................... from (1) ..= arcsin [ 2u ] + C ..= arcsin [ 2( x - 1/2 ) ] + C ..= arcsin ( 2x - 1 ) + C

  2. TheRealMeeeee
    • 2 years ago
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    do this help!!

  3. TheRealMeeeee
    • 2 years ago
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    omg do this help???????????????!!!!!!!!!

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