integral from 0 to 3pi of e^tsqrt(6)

解答

\int_{0}^{3 π} e^{t} 6 d t

6 (e^{3 π} - 1)

十进制

30350.76471 \dots

求解步骤

\int_{0}^{3 π} e^{t} 6 d t

提出常数:

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

= 6 \cdot \int_{0}^{3 π} e^{t} d t

使用积分常见定则:

\int e^{t} d t = e^{t}

= 6 [e^{t}]_{0}^{3 π}

带入上下限计算后得:

e^{3 π} - 1

= 6 (e^{3 π} - 1)

\int_{0}^{2} 4 x^{2} - 8 x + 5 d x

\int_{3}^{4} \frac{3}{x - 3} d x

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

\int_{1.5}^{3} \frac{1}{8} x d x

\int_{1}^{e} (14 + ln (x))^{2} d x