Question

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

Answer 1

ok


Hemant answered 4 years ago

Standard Formula : ∫ [ 1 / √( a² - u² ) ] du = arcsin ( u / a ) ........... (1)
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I = ∫ [ 1 / √( x - x² ) ] dx ............. (2)
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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

Answer 2

do this help!!

Answer 3

omg do this help???????????????!!!!!!!!!