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Grade 11Integral Calculus

Integral of : cosx dx. =
———————
[cosx/2 +sinx/2]^5

Question image for Integral of : cosx dx. = ——————— [cosx/2 +sinx/2]

Myra

6 Years agoGrade 11

1 Answer

Myra

6 Years ago

Let cosx= (cosx/2-sinx/2)(cosx/2+sinx/2)

After substituting

∫(cosx/2-sinx/2) dx

——————————

(cosx/2+sinx/2)^4

Let (cosx/2+sinx/2) = t

By differentiating

[cosx/2 - sinx/2] dx= 2dt

After substitution

2∫dt

——— =

t^4

After integration

-2/3( t^-3) + C

-2/3 [ sinx/2 +cosx/2]^-3 +C

t^4

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