integral from 0 to 4 of (5-x)sqrt(x)

해법

\int_{0}^{4} (5 - x) x d x

\frac{208}{15}

십진법

13.86666 \dots

솔루션 단계

\int_{0}^{4} (5 - x) x d x

(5 - x) x

확대한다:

5 x - x^{\frac{3}{2}}

= \int_{0}^{4} 5 x - x^{\frac{3}{2}} d x

합계 규칙 적용:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{4} 5 x d x - \int_{0}^{4} x^{\frac{3}{2}} d x

\int_{0}^{4} 5 x d x = \frac{80}{3}

\int_{0}^{4} x^{\frac{3}{2}} d x = \frac{64}{5}

= \frac{80}{3} - \frac{64}{5}

\frac{80}{3} - \frac{64}{5}

간소화하다 :

\frac{208}{15}

= \frac{208}{15}