Home > Calculus > Integrals of Polynomial functions

What is the integral of #sqrt(1-x^2)#?

Answer 1

Hint: First, apply trigonometric substitution. This question is in the form #sqrt(a^2-x^2)#. So you let x = a sinx (a in this case is 1) then take the derivative of x. Plug it back in the question #int sqrt(1-x^2) dx#
You will have to use the half-angle identity after.
Integrate. You will get an indefinite integral.
Set up a right triangle to find the value for the indefinite integral.

I hope this video would help clear things up.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emily Ammerman

The integral of sqrt(1-x^2) is equal to (1/2)(xsqrt(1-x^2) + arcsin(x)) + C, where C is the constant of integration.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.