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integral sqrt(1-cos(ax)) dx

integral sqrt(1-cos(ax)) dx

Grade:12

1 Answers

Rathod Shankar AskiitiansExpert-IITB
69 Points
10 years ago

cos(2ax)=1-2sin2(ax)

cos(ax)=1-2sin2(ax/2)

1-cos(ax)=2sin2(ax/2)

sqrt(1-cos(x))=+[sqrt(2)] * sin(x/2)  or -[sqrt(2)] * sin(x/2)

 

integral sqrt(1-cos(ax)) dx =integral{ [sqrt(2)] * sin(x/2) }dx 

                                                 = -2 *sqrt(2)*cos(ax/2) +C       or                                             =2*sqrt(2)*cos(ax/2) +C   (use both sines + and -)
 

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