integral from-1 to 0 of-cos(npix)

解答

\int_{- 1}^{0} - cos (nπ x) d x

0

求解步骤

\int_{- 1}^{0} - cos (nπ x) d x

提出常数:

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

= - \int_{- 1}^{0} cos (nπ x) d x

使用换元积分法

= - \int_{- πn}^{0} \frac{cos ( u )}{πn} d u

提出常数:

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

= - \frac{1}{πn} \cdot \int_{- πn}^{0} cos (u) d u

使用积分常见定则:

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

= - \frac{1}{πn} [sin (u)]_{- πn}^{0}

带入上下限计算后得:

0

= - \frac{1}{πn} \cdot 0

化简

= 0

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