Calculate the double integrals

Question 4. Calculate the double integrals. a) JRIcosydA, R is bounded by {y =0}, {y = x } and {x = 1}. b) [x2 + 2ydA, R is bounded by {y = x}, {y = x3 } and {x > 0}. c) frydA, R in the first, quadrant bounded by the circle {a + y? = 1}. Question 5. Find the volume of the region enclosed by the paraboloid {z = x2 + y? + 1} and the planes { =0}, {y =0}, {= =0}, and {x ty = 2}. Question 6. Use polar coordinates to evaluate the double integrals. a) JarrydA, R is the top half of the disk with center the origin and radius 5. b) [2x - ydA, R is the region in the first quadrant enclosed by the circle { + y = 4) and the lines {x =0} and {y = x}. c) J sin(x2 +y' )dA, R is the region in the first quadrant between the circles with center the origin and radii 1 and 3