Final answer to the problem
$r\arcsin\left(\frac{r}{r}\right)-r\arcsin\left(\frac{0}{r}\right)$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
The integral of a function times a constant ($r$) is equal to the constant times the integral of the function
Learn how to solve definite integrals problems step by step online.
$r\int_{0}^{r}\frac{1}{\sqrt{r^2-x^2}}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function r/((r^2-x^2)^(1/2)) from 0 to r. The integral of a function times a constant (r) is equal to the constant times the integral of the function. Apply the well-known integration formula: \displaystyle\int\frac{1}{\sqrt{a^2-x^2}}dx = \arcsin\left(\frac{x}{a}\right). Cancel exponents 2 and 1. Evaluate the definite integral.
Final answer to the problem
$r\arcsin\left(\frac{r}{r}\right)-r\arcsin\left(\frac{0}{r}\right)$
