What is the proper solution for these problems?

Subject: Calculus

Reduce the curve to standard form if possible, plot the curve properly, indicate the points of intersection and find the area between curves. 1. Find the area bounded by the curve y = 4x - x2 and the lines x = 0 and y = 4. Solve in two ways. 2. Find the area bounded by the curve y = 4x - x2 and the lines x = -2 and y = 4. 3. Find the each of the areas bounded by the curves y = x3 - 4x and y = x2 + 2x. 4. Find the area, in the first quadrant, bounded by the lines x = 2a, y = 4a, the axes and the curve x y = a3. 5. Find the area between the curves 2y2 + 4x + y = 0, y = 2x. 6. Find the area between the curves y" = 2x +3, y = x. 7. Find the area under one arch of the curve y = cos= x. 8. Find the area bounded by the curves and lines: y2 = 7 (2-x)3' x = -2, x = 0. 9. Find the area bounded by the curves and lines: xy = a2, y=0, x=a, x=2a. 10. Find the area bounded by the curve aly? = x2 (a2 - x2)