Evaluate the following definite Integrals:

Here the equation is of form that a quadratic equation is in the root so now to solve this make the equation in the root in the form of a²–x²,a²+x²

Here

=4–(x–1)²

=2²–(x–1)²

Now just recall a formula that is derivative of

Here a=2 and x =x–1

Now we get