integral from 1 to 2 of (v^4+3v^5)/(v^3)

解答

\int_{1}^{2} \frac{v ^{4} + 3 v ^{5}}{v ^{3}} d v

\frac{17}{2}

十进制

8.5

求解步骤

\int_{1}^{2} \frac{v ^{4} + 3 v ^{5}}{v ^{3}} d v

化简

\frac{v ^{4} + 3 v ^{5}}{v ^{3}} : v (3 v + 1)

= \int_{1}^{2} v (3 v + 1) d v

乘开

v (3 v + 1) : 3 v^{2} + v

= \int_{1}^{2} 3 v^{2} + v d v

使用积分加法定则:

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

= \int_{1}^{2} 3 v^{2} d v + \int_{1}^{2} v d v

\int_{1}^{2} 3 v^{2} d v = 7

\int_{1}^{2} v d v = \frac{3}{2}

= 7 + \frac{3}{2}

化简

7 + \frac{3}{2} : \frac{17}{2}

= \frac{17}{2}

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