integral from 0 to pi/3 of cos(4x)

解答

\int_{0}^{\frac{π}{3}} cos (4 x) d x

- \frac{3}{8}

十进制

- 0.21650 \dots

求解步骤

\int_{0}^{\frac{π}{3}} cos (4 x) d x

使用换元积分法

= \int_{0}^{\frac{4 π}{3}} cos (u) \frac{1}{4} d u

提出常数:

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

= \frac{1}{4} \cdot \int_{0}^{\frac{4 π}{3}} cos (u) d u

使用积分常见定则:

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

= \frac{1}{4} [sin (u)]_{0}^{\frac{4 π}{3}}

带入上下限计算后得:

- \frac{3}{2}

= \frac{1}{4} (- \frac{3}{2})

化简

= - \frac{3}{8}

n = 1 \sum \infty (- 1)^{n + 1} \frac{2}{n + 1}

d er i v a t i v e y = 8 x e^{x}

\frac{d}{d z} (\frac{2 z ^{6} + 2}{1 z ^{2} + 5})

n = 1 \sum \infty (\frac{e}{n})^{2 n}

\int cos^{4} (1) d x