Let R be the region in R^2 enclosed in the circle x^2 +y^2 = 1 and below the parabola y = 1x^2.

(a) Sketch the region R. Find the points of intersection of the line and the circle and indicate them on your sketch.

(b) Is R a Type I region? If yes, describe it as a Type I region. If not, describe it as a union of Type I regions. Use set builder notation.

(c) Is R a Type II region? If yes, describe it as a Type II region. If not, describe it as a union of Type II regions. Use set builder notation.

(d) Calculate the integral _R (x^2y^2 )dA

i. by using the order of integration dy/dx

ii. by using the order of integration dx/dy