💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

Problem 64 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^a_0 x\sqrt{a^2 - x^2} \, dx $

Answer

$\int_{0}^{a} x \sqrt{a^{2}-x^{2}} d x=\frac{1}{3} a^{3}$

More Answers

Discussion

You must be signed in to discuss.

Video Transcript

we know that Are you? Convene what's under the square root, which is a scored minus X squared which means r D X is now negative 1/2 do you over acts which means our bounds are now going to be from a squared to zero because we know a is a squared minus a score which is zero and be a zero squared plus a scored, which is simply just gonna give us a squared. Let's let us use the power rule, which means we increase the expert by one and we divide by the new exponents. Now we can simply plug in our bounds. This gives us 1/3 a cute