integral from 0 to pi/2 of 1+cos(2y)

解答

\int_{0}^{\frac{π}{2}} 1 + cos (2 y) d y

\frac{π}{2}

十进制

1.57079 \dots

求解步骤

\int_{0}^{\frac{π}{2}} 1 + cos (2 y) d y

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

\int_{0}^{\frac{π}{2}} 1 d y = \frac{π}{2}

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

= \frac{π}{2} + 0

化简

= \frac{π}{2}

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