Integration Question #2

I came across the integral a few days ago. Pretty interesting, many ways to solve this integral, be it graphically or by substitution.

\int_a^b \sqrt{(x-a)(b-x)} dx =?

Answer: \pi \frac{(a-b)^2}{4}

Hint: Consider the graph of y = \sqrt{(x-a)(b-x)}, it should give a semicircle which centre is (\frac{a+b}{2},0)

Leave a Comment

Contact Us

CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

Not readable? Change text. captcha txt

Start typing and press Enter to search