定積分・広義積分計算機

この計算機は、定積分（すなわち上下限のある積分）を、広義積分も含めて、解法手順を示しながら計算を試みます。

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Integrate with respect to:

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

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If you need `oo`, type inf.

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Solution

Your input: calculate $$$\int_{0}^{e}\left( e^{\frac{x}{2}} - 2 \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\left(e^{\frac{x}{2}} - 2\right)d x}=- 2 x + 2 e^{\frac{x}{2}}$$$ (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.

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

$$$\left(- 2 x + 2 e^{\frac{x}{2}}\right)|_{\left(x=0\right)}=2$$$

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

Answer: $$$\int_{0}^{e}\left( e^{\frac{x}{2}} - 2 \right)dx=- 2 e - 2 + 2 e^{\frac{e}{2}}\approx 0.349131492901035$$$

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定積分・広義積分計算機

定積分と広義積分を手順を追って計算する

Solution