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Evaluate-0-1-2-1-x-2-dx-By-direct-integration-and-by-expanding-as-a-power-series-




Question Number 8375 by tawakalitu last updated on 09/Oct/16
Evaluate : ∫_0 ^(1/2) (√(1 − x^2 )) dx  By direct integration and by expanding  as a power series.
$$\mathrm{Evaluate}\::\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \sqrt{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$$$\mathrm{By}\:\mathrm{direct}\:\mathrm{integration}\:\mathrm{and}\:\mathrm{by}\:\mathrm{expanding} \\ $$$$\mathrm{as}\:\mathrm{a}\:\mathrm{power}\:\mathrm{series}. \\ $$

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