Evaluate the integral by interpreting it in terms of area

Question

₀ ∫¹  x+sqrt(1-x^2) dx

Answer 1

The first part of the integrand is y=x and so the area under that line, on interval [0,1] is ½.

 

The second part of the integrand is y = √(1-x²)  or x²+y² = 1, a unit circle; now...what's the area under the circle in the first quadrant?  Get it?