Calculadora de Integrais Definidas e Impróprias

A calculadora tentará calcular a integral definida (isto é, com limites), inclusive no caso impróprio, com os passos mostrados.

Enter a function:

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

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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Calculadora de Integrais Definidas e Impróprias

Calcule integrais definidas e impróprias passo a passo

Solution