integral from 0 to pi/2 of 243sin(θ)

解答

\int_{0}^{\frac{π}{2}} 243 sin (θ) d θ

243

求解步骤

\int_{0}^{\frac{π}{2}} 243 sin (θ) d θ

提出常数:

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

= 243 \cdot \int_{0}^{\frac{π}{2}} sin (θ) d θ

使用积分常见定则:

\int sin (θ) d θ = - cos (θ)

= 243 [- cos (θ)]_{0}^{\frac{π}{2}}

带入上下限计算后得:

1

= 243 \cdot 1

化简

= 243

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