定积分与广义积分计算器

该计算器将尝试计算定积分（即带上下限的积分），包括广义积分，并显示求解步骤。

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Integrate with respect to:

Enter a lower limit:

If you need `-oo`, type -inf.

Enter an upper limit:

If you need `oo`, type inf.

Please write without any differentials such as `dx`, `dy` etc.

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Solution

Your input: calculate $$$\int_{0}^{3}\left( \sqrt{2} x^{3} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\sqrt{2} x^{3} d x}=\frac{\sqrt{2} x^{4}}{4}$$$ (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.

$$$\left(\frac{\sqrt{2} x^{4}}{4}\right)|_{\left(x=3\right)}=\frac{81 \sqrt{2}}{4}$$$

$$$\left(\frac{\sqrt{2} x^{4}}{4}\right)|_{\left(x=0\right)}=0$$$

$$$\int_{0}^{3}\left( \sqrt{2} x^{3} \right)dx=\left(\frac{\sqrt{2} x^{4}}{4}\right)|_{\left(x=3\right)}-\left(\frac{\sqrt{2} x^{4}}{4}\right)|_{\left(x=0\right)}=\frac{81 \sqrt{2}}{4}$$$

Answer: $$$\int_{0}^{3}\left( \sqrt{2} x^{3} \right)dx=\frac{81 \sqrt{2}}{4}\approx 28.6378246380552$$$

定积分与广义积分计算器

逐步计算定积分和广义积分

Solution