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integrate sin^8x.dx

integrate sin^8x.dx

Grade:12

2 Answers

AskiitianExpert Shine
10 Points
12 years ago

Hi

Split the sin8x dx into sin2x sin6 x dx, and mutiply the numerator and denominator by 3cosx,

Hence the expression becomes 3sin2x sin6x  cosx dx / 3cosx ..  now take sin3x = t and substitute in the expression. We made this substitution because on differentiating sin3x , we get 3sin2x cosx dx, hence we can directly substitute it in the expresssion.

After substitution we get, t2dt/3 (1-t2/3)1/2 . Again make a substitution of y2 = 1-t2/3 .

Try at all times , to somehow eliminate the denominator term, wen u get to that step, use the formulas specified for particular forms.

Nishavak
14 Points
3 years ago
Use double angles.Calculative but easy sum.Just put sin^2(x) as (1-cos2x)/2. And go with the flow. You will reach ur answer pretty quick, provided you should have faster calculation speed.

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