integral from 1 to 9 of 4sqrt(x)

解答

\int_{1}^{9} 4 x d x

\frac{208}{3}

十进制

69.33333 \dots

求解步骤

\int_{1}^{9} 4 x d x

提出常数:

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

= 4 \cdot \int_{1}^{9} x d x

使用幂法则

= 4 [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{9}

带入上下限计算后得:

\frac{52}{3}

= 4 \cdot \frac{52}{3}

化简

= \frac{208}{3}

\int - 2 π cos^{4} (π x) sin^{5} (π x) d x

\int 5 x 2 x + 3 d x

\int \frac{1}{x ( 1 + x ) ^{3}} d x

x \to 2 lim (a x^{2} - 2 b x + 1)

y^{^{'}} - \frac{9}{x} y = \frac{( y ^{5} )}{x ^{8}}