Final answer to the problem
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- Weierstrass Substitution
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Apply the formula: $\int\frac{n}{a}dx$$=n\int\frac{1}{a}dx$, where $a=\sqrt{r^2-x^2}$ and $n=r$
Learn how to solve intégrales définies problems step by step online.
$r\int_{0}^{r}\frac{1}{\sqrt{r^2-x^2}}dx$
Learn how to solve intégrales définies problems step by step online. int(r/((r^2-x^2)^(1/2)))dx&0&r. Apply the formula: \int\frac{n}{a}dx=n\int\frac{1}{a}dx, where a=\sqrt{r^2-x^2} and n=r. Apply the formula: \int\frac{n}{\sqrt{a-b^2}}dx=n\arcsin\left(\frac{b}{\sqrt{a}}\right)+C, where a=r^2, b=x and n=1. Apply the formula: \left(x^a\right)^b=x, where a=2, b=1, x^a^b=\sqrt{r^2}, x=r and x^a=r^2. Apply the formula: \left[x\right]_{a}^{b}=eval\left(x,b\right)-eval\left(x,a\right)+C, where a=0, b=r and x=r\arcsin\left(\frac{x}{r}\right).
