1) (5 pts) Let F(z) = |n/1-x2 + arcsin(z) a) Compute F(r) and show that it simplifies to 1- (recall that the derivative of arcsin(x) is 7 ) This means, for example, that Jo Vi-rī dr = F(1)-F(0) arcsin(1) . But, I also showed in class that this is more easily computed by realizing that Jo vi-x* dz is just the area of one quarter of the unit circle. b) Use F to compute 05 VI- dz. Give the approximate value of the integral to at least 3 decimal places. Also, give the exact value in the form of a sum of two "simplified" terms, one of which includes a v3 and the other includes arcsin(0.5) c) Sketch a picture of the unit circle in the first quadrant, and indicate the region whose dz. Draw in the line segment from the origin to the point area is eqlal to on the circle whose r-coordinate is 0.5. Show that this divides the region into two parts whose areas are the two terms from your exact answer to (b)