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\int_{-1}^{1}\sqrt{1+x^2}dx

Integrate (1+x^2)^0.5 from -1 to 1

Answer

$\sqrt{5}$

Step-by-step explanation

Problem

$\int_{-1}^{1}\sqrt{1+x^2}dx$
1

Solve the integral $\int\sqrt{x^2+1}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=1\tan\left(\theta\right) \\ dx=\sec\left(\theta\right)^2d\theta\end{matrix}$

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Answer

$\sqrt{5}$