Give the correct answer and solve the given equation Evaluate displaystyleint{x}^{3}{left({sqrt[{3}]{{{1}-{x}^{2}}}}right)}{left.{d}{x}right.}

Emily-Jane Bray 2020-11-11 Answered
Give the correct answer and solve the given equation Evaluate x3(1x23)dx
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Expert Answer

l1koV
Answered 2020-11-12 Author has 100 answers
We have to find x3(1x23)dx
Aplly substitution u=1x2 gives us du=2xdxandx=(1u)
x21x23dx=x21x23(xdx)
=(1u)u22du
=12(1u)u3 du
=12u3u43du
=12(u3duu43du)[Apply the sum rule of integration]
=12(u13+113+1u43+143+1)[xndx=xn+1n+1,n1]
=12(34u4337u73)
=12(34(1x2)4337(1x2)43)[u=1x2]
=3(1x2)73143(1x2)438
=C(1x2)4312x2+956
where C is an integrating constant.
The finally answer is
x3(1x23)dx=C(1x2)4
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