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受欢迎的微积分 >

integral from 0 to 1 of x^7(1+x^8)^7

解答

\int_{0}^{1} x^{7} (1 + x^{8})^{7} d x

解答

\frac{255}{64}

+1

十进制

3.984375

求解步骤

\int_{0}^{1} x^{7} (1 + x^{8})^{7} d x

使用换元积分法

= \int_{1}^{2} \frac{u ^{7}}{8} d u

提出常数:

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

= \frac{1}{8} \cdot \int_{1}^{2} u^{7} d u

使用幂法则

= \frac{1}{8} [\frac{u ^{8}}{8}]_{1}^{2}

带入上下限计算后得:

\frac{255}{8}

= \frac{1}{8} \cdot \frac{255}{8}

化简

= \frac{255}{64}

作图

流行的例子

integral of (x+9)/(sqrt(1-2x-2x^2))

\int \frac{x + 9}{1 - 2 x - 2 x ^{2}} d x

integral from 0 to 1 of y/(e^{9y)}

\int_{0}^{1} \frac{y}{e ^{9 y}} d y

斜率 y=2+4x^2-2x^3

s l o p e y = 2 + 4 x^{2} - 2 x^{3}

\int - 3 d x

y^{''}+5y=4t^4,y(0)=0,y^'(0)=0

y^{^{''}} + 5 y = 4 t^{4}, y (0) = 0, y^{^{'}} (0) = 0