integral from-2 to 2 of e^{u+2}

解答

\int_{- 2}^{2} e^{u + 2} d u

e^{4} - 1

十进制

53.59815 \dots

求解步骤

\int_{- 2}^{2} e^{u + 2} d u

e^{u + 2} = e^{2} e^{u}

= \int_{- 2}^{2} e^{2} e^{u} d u

提出常数:

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

= e^{2} \cdot \int_{- 2}^{2} e^{u} d u

使用积分常见定则:

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

= e^{2} [e^{u}]_{- 2}^{2}

带入上下限计算后得:

e^{2} - \frac{1}{e ^{2}}

= e^{2} (e^{2} - \frac{1}{e ^{2}})

化简

= e^{4} - 1

\int_{1}^{2} \frac{2 x ^{2} + 1}{x} d x

\int_{1}^{7} (x^{2} - 8 x + 16)^{2} d x

\int_{0}^{3} 2^{3 x} d x

\int_{0}^{2 π} - 2 sin^{2} (t) d t

\int_{- 3}^{3} \frac{sin ( x )}{1 + x ^{2}} d x