Question

Evaluate the integral by interpreting it in terms of areas. (integral upper(2) lower(-2)) sqrt(4-x^2)dx

Answer 1

if u take the equation of the circle \[x ^{2}+y ^{2}=2^{2}\] then u will get \[y=\sqrt{4-x ^{2}}\]. and the given integral is eqivalent to the area of the upper half of the cicle because only in the upper half y is +ve. and the ans. will be \[1/2*\pi*2^{2}=2\pi\]

Answer 2

ohhh thank u so much. i kept the 4 and forgot to square it so i had my radius to be 4.thanks a lot