integral from 0 to pi/2 of y+y^2cos(x)

解答

\int_{0}^{\frac{π}{2}} y + y^{2} cos (x) d x

\frac{π y}{2} + y^{2}

求解步骤

\int_{0}^{\frac{π}{2}} y + y^{2} cos (x) d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{\frac{π}{2}} y d x + \int_{0}^{\frac{π}{2}} cos (x) y^{2} d x

\int_{0}^{\frac{π}{2}} y d x = \frac{π y}{2}

\int_{0}^{\frac{π}{2}} cos (x) y^{2} d x = y^{2}

= \frac{π y}{2} + y^{2}

\int_{\frac{π}{3}}^{π} x cos (2 x) d x

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