integral from-pi to 0 of 3cos(nx)

解答

\int_{- π}^{0} 3 cos (n x) d x

0

求解步骤

\int_{- π}^{0} 3 cos (n x) d x

提出常数:

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

= 3 \cdot \int_{- π}^{0} cos (n x) d x

使用换元积分法

= 3 \cdot \int_{- πn}^{0} \frac{cos ( u )}{n} d u

提出常数:

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

= 3 \cdot \frac{1}{n} \cdot \int_{- πn}^{0} cos (u) d u

使用积分常见定则:

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

= 3 \cdot \frac{1}{n} [sin (u)]_{- πn}^{0}

化简

3 \cdot \frac{1}{n} [sin (u)]_{- πn}^{0} : \frac{3}{n} [sin (u)]_{- πn}^{0}

= \frac{3}{n} [sin (u)]_{- πn}^{0}

带入上下限计算后得:

0

= \frac{3}{n} \cdot 0

化简

= 0

\int_{0}^{20} - 0.4 x^{2} + 1000 - 840 d x

\int_{1}^{4} x e^{x^{2}} d x

\int_{2}^{4} 5 x ln (x) d x

\int_{2}^{3} e^{x^{2}} d x

\int_{0}^{1} x - x^{2} + 1 d x