integral of θsin(θ^2)

解答

\int θ sin (θ^{2}) d θ

- \frac{1}{2} cos (θ^{2}) + C

求解步骤

\int θ sin (θ^{2}) d θ

使用换元积分法

= \int \frac{sin ( u )}{2} d u

提出常数:

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

= \frac{1}{2} \cdot \int sin (u) d u

使用积分常见定则:

\int sin (u) d u = - cos (u)

= \frac{1}{2} (- cos (u))

u = θ^{2}

代回

= \frac{1}{2} (- cos (θ^{2}))

化简

= - \frac{1}{2} cos (θ^{2})

解答补常数

= - \frac{1}{2} cos (θ^{2}) + C

x \to 6 + lim (sec (\frac{π x}{4}))

\int_{- 1}^{1} x^{2} - 2 d x

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