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人気のある微分積分 >

integral from 0 to r of br^3+cr^2

解

\int_{0}^{r} b r^{3} + c r^{2} d r

解

\frac{b r ^{4}}{4} + \frac{c r ^{3}}{3}

解答ステップ

\int_{0}^{r} b r^{3} + c r^{2} d r

総和規則を適用する:

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

= \int_{0}^{r} b r^{3} d r + \int_{0}^{r} c r^{2} d r

\int_{0}^{r} b r^{3} d r = \frac{b r ^{4}}{4}

\int_{0}^{r} c r^{2} d r = \frac{c r ^{3}}{3}

= \frac{b r ^{4}}{4} + \frac{c r ^{3}}{3}

人気の例

integral from n to infinity of 1/(x^5)

\int_{n}^{\infty} \frac{1}{x ^{5}} d x

integral from 3 to 4 of (2(1+x))/(27)

\int_{3}^{4} \frac{2 ( 1 + x )}{27} d x

integral from-infinity to 0 of 4^r

\int_{- \infty}^{0} 4^{r} d r

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

integral from 0 to 6 of 4/(sqrt(6-x))

\int_{0}^{6} \frac{4}{6 - x} d x