integral from-ln(4) to 0 of 2sqrt(3)e^t

解答

\int_{- l n (4)}^{0} 23 e^{t} d t

\frac{3 3}{2}

十进制

2.59807 \dots

求解步骤

\int_{- l n (4)}^{0} 23 e^{t} d t

提出常数:

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

= 23 \cdot \int_{- l n (4)}^{0} e^{t} d t

使用积分常见定则:

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

= 23 [e^{t}]_{- l n (4)}^{0}

化简

ln (4) : 2 ln (2)

= 23 [e^{t}]_{- 2 l n (2)}^{0}

带入上下限计算后得:

\frac{3}{4}

= 23 \frac{3}{4}

化简

= \frac{3 3}{2}

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