Math  /  Calculus

Question01x10x2dx\int_{0}^{1} x \sqrt{10-x^{2}} d x

Studdy Solution
Calculate the definite integral:
=12(23×103/223×93/2) = \frac{1}{2} \left( \frac{2}{3} \times 10^{3/2} - \frac{2}{3} \times 9^{3/2} \right)
=13(103/293/2) = \frac{1}{3} \left( 10^{3/2} - 9^{3/2} \right)
=13(1000729) = \frac{1}{3} \left( \sqrt{1000} - \sqrt{729} \right)
=13(101027) = \frac{1}{3} \left( 10\sqrt{10} - 27 \right)
Thus, the value of the integral is:
13(101027) \boxed{\frac{1}{3} \left( 10\sqrt{10} - 27 \right)}

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