Question

Evaluate the integral from 0 to 5 of
(x-sqrt(25-x^2))dx by interpreting it in terms of an area.

Answer 1

\[\int_0^5 \left(x-\sqrt{25-x^2}\right) dx = \int_0^5 x dx - \int_0^5\sqrt{25-x^2}dx\]

Answer 2

Notice that first integral gives u area under y = x line which is a triangle

Answer 3

and the second integral is simply the area of circle x^2 + y^2 = 25 in first quadrant

Answer 4

still stuck on this ?