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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Solution

Your input: calculate $$$\int_{0}^{\frac{\pi}{4}}\left( \tan^{4}{\left(x \right)} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\tan^{4}{\left(x \right)} d x}=x + \frac{\tan^{3}{\left(x \right)}}{3} - \tan{\left(x \right)}$$$ (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.

$$$\left(x + \frac{\tan^{3}{\left(x \right)}}{3} - \tan{\left(x \right)}\right)|_{\left(x=\frac{\pi}{4}\right)}=- \frac{2}{3} + \frac{\pi}{4}$$$

$$$\left(x + \frac{\tan^{3}{\left(x \right)}}{3} - \tan{\left(x \right)}\right)|_{\left(x=0\right)}=0$$$

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

Answer: $$$\int_{0}^{\frac{\pi}{4}}\left( \tan^{4}{\left(x \right)} \right)dx=- \frac{2}{3} + \frac{\pi}{4}\approx 0.118731496730782$$$

定积分与广义积分计算器

逐步计算定积分和广义积分

Solution