Step-by-step Solution

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

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$2.295587149392638$

Step-by-step explanation

Problem to solve:

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

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

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

Substituting in the original integral, we get

$\int_{-1}^{1}\sqrt{1+\left(1\tan\left(\theta\right)\right)^2}\sec\left(\theta\right)^2d\theta$

$2.295587149392638$
$\int_{-1}^{1}\sqrt{1+x^2}dx$

Main topic:

Integration by trigonometric substitution

~ 1.25 seconds

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