Question

Evaluate the definite integral wrt x that represents the area of a circle that is bounded by the positive x and y axes.

Answer 1

Meaning the 1st quadrant only?

Answer 2

That's right.

Answer 3

that's the integral from 0 to r of sqrt(r^2 - x^2), which evaluates to pi*r^2/4

Answer 4

can be evaluated with a substitution of x = rsin(t)

Answer 5

Might as well just use the unit circle, drop the r.