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Question
hi
i've some problems to solve this integral
x^3sqrt(4 -x^2)dx
i should solve it using trigonometric sub.
this what i did
x=2sin@
dx=2cosd@
2*(2sin@)^3*cos^2@ d@
then i integrated but i don't get the right answer =(
your help is very much appreciated
Now gives the equation is ∫2sin³Θ*cos²Θ dΘ, make sin²(Θ) into 1 - cos²Θ.
Rewriting what we have gives ∫2(sinΘ*cos²Θ dΘ - sinΘcos^4(Θ))dΘ.
If we then say that u = cosΘ, du = -sinΘ dΘ.
This makes the integral ∫2(-u² - u^4)du, and that is only polynomial integration.
Integrate and put back in u = cosΘ to get to the answer.
This gives 2(-cos^3(Θ)/3 - cos^5(Θ)/5) + C.
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