Final Answer
$\frac{-\sqrt{\left(a^2-x^2\right)^{3}}}{3}+C_0$
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Step-by-step Solution
Problem to solve:
$\int x\sqrt{a^2-x^2}dx$
Specify the solving method
1
We can solve the integral $\int x\sqrt{a^2-x^2}dx$ by applying integration method of trigonometric substitution using the substitution
$x=a\sin\left(\theta \right)$
Learn how to solve integrals with radicals problems step by step online.
$x=a\sin\left(\theta \right)$
Learn how to solve integrals with radicals problems step by step online. Integrate int(x(a^2-x^2)^1/2)dx. We can solve the integral \int x\sqrt{a^2-x^2}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Simplifying.
Final Answer
$\frac{-\sqrt{\left(a^2-x^2\right)^{3}}}{3}+C_0$