정적분 및 가적분 계산기

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Solution

Your input: calculate $$$\int_{1}^{9}\left( \frac{- x^{\frac{3}{2}} + 4 x^{5} - 3}{x^{2}} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{- x^{\frac{3}{2}} + 4 x^{5} - 3}{x^{2}} d x}=\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}$$$ (for steps, see indefinite integral calculator)

According to the Fundamental Theorem of Calculus, $$$\int_a^b F(x) dx=f(b)-f(a)$$$, so just evaluate the integral at the endpoints, and that's the answer.

$$$\left(\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}\right)|_{\left(x=9\right)}=\frac{19666}{3}$$$

$$$\left(\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}\right)|_{\left(x=1\right)}=2$$$

$$$\int_{1}^{9}\left( \frac{- x^{\frac{3}{2}} + 4 x^{5} - 3}{x^{2}} \right)dx=\left(\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}\right)|_{\left(x=9\right)}-\left(\frac{- 2 x^{\frac{3}{2}} + x^{5} + 3}{x}\right)|_{\left(x=1\right)}=\frac{19660}{3}$$$

Answer: $$$\int_{1}^{9}\left( \frac{- x^{\frac{3}{2}} + 4 x^{5} - 3}{x^{2}} \right)dx=\frac{19660}{3}\approx 6553.33333333333$$$

정적분 및 가적분 계산기

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Solution