Learn how to solve addition of numbers problems step by step online. Integrate int((a^2-v^2)^(1/2))dv. We can solve the integral \int\sqrt{a^2-v^2}dv by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dv, we need to find the derivative of v. We need to calculate dv, we can do that by deriving the equation above. Substituting in the original integral, we get. Factor the polynomial a^2-a^2\sin\left(\theta \right)^2 by it's greatest common factor (GCF): a^2.

Integrate int((a^2-v^2)^(1/2))dv