integral from 0 to pi/4 of 2cos(x)

解答

\int_{0}^{\frac{π}{4}} 2 cos (x) d x

2

十进制

1.41421 \dots

求解步骤

\int_{0}^{\frac{π}{4}} 2 cos (x) d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{\frac{π}{4}} cos (x) d x

使用积分常见定则:

\int cos (x) d x = sin (x)

= 2 [sin (x)]_{0}^{\frac{π}{4}}

带入上下限计算后得:

\frac{1}{2}

= 2 \cdot \frac{1}{2}

化简

= 2

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