integral from 0 to pi of 7/3 sin(x)

解答

\int_{0}^{π} \frac{7}{3} sin (x) d x

\frac{14}{3}

十进制

4.66666 \dots

求解步骤

\int_{0}^{π} \frac{7}{3} sin (x) d x

提出常数:

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

= \frac{7}{3} \cdot \int_{0}^{π} sin (x) d x

使用积分常见定则:

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

= \frac{7}{3} [- cos (x)]_{0}^{π}

带入上下限计算后得:

2

= \frac{7}{3} \cdot 2

化简

= \frac{14}{3}

\int_{0}^{2} x (1 - \frac{1}{2} x) d x

\int_{0}^{8} 16 x - x^{2} d x

\int_{1}^{2} (5 x^{2} - 3) d x

\int_{0}^{5} sin (t^{2}) d t

\int_{3}^{6} 3 d x