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Question Number 85717 by M±th+et£s last updated on 24/Mar/20

$${\int }_0^2{x}^4\sqrt{1-x^2}dx$$$$$$$${\int }_0^1{x}^{10}(1-x^n)dx$$$$$$

Answered by mind is power last updated on 24/Mar/20

$${\int }_0^1{x}^4\sqrt{1-x^2}dx$$$$={\int }_0^{\frac{\pi }{2}}{sin}^4\left(t\right){cos}^2\left(t\right)dt$$$$={\int }_0^{\frac{\pi }{2}}\frac{{sin}^2\left(2t\right)}{4}{sin}^2\left(t\right)dt$$$$easy$$$$2)=\frac{1}{10}-\frac{1}{n+11}=\frac{n+1}{10(n+11)}$$

Commented by M±th+et£s last updated on 24/Mar/20

$$thankyousir$$

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