integral from 0 to pi/3 of xsin(9x)

解答

\int_{0}^{\frac{π}{3}} x sin (9 x) d x

\frac{π}{27}

十进制

0.11635 \dots

求解步骤

\int_{0}^{\frac{π}{3}} x sin (9 x) d x

使用分布积分法

= [\frac{1}{9} (- x cos (9 x) - 9 \cdot \int - \frac{1}{9} cos (9 x) d x)]_{0}^{\frac{π}{3}}

\int - \frac{1}{9} cos (9 x) d x = - \frac{1}{81} sin (9 x)

= [\frac{1}{9} (- x cos (9 x) - 9 (- \frac{1}{81} sin (9 x)))]_{0}^{\frac{π}{3}}

化简

[\frac{1}{9} (- x cos (9 x) - 9 (- \frac{1}{81} sin (9 x)))]_{0}^{\frac{π}{3}} : [\frac{1}{9} (- x cos (9 x) + \frac{1}{9} sin (9 x))]_{0}^{\frac{π}{3}}

= [\frac{1}{9} (- x cos (9 x) + \frac{1}{9} sin (9 x))]_{0}^{\frac{π}{3}}

带入上下限计算后得:

\frac{π}{27}

= \frac{π}{27}

d er i v a t i v e \frac{x ^{2}}{7 + 8 x}

\frac{d}{d x} (8 + x)

t an g e n t f (x) = ln (x), at x = 6

y^{^{''}} + 4 y^{^{'}} + 40 y = 50 cos (8 t)

\int \frac{- 9000}{( 3 x + 50 ) ^{2}} d x