Please solve the following problems as soon as you can:

Q1)

Find the total area of the shaded regions bounded between the curves y = x + 2e\"2 and y = xe'd2 + 2 on the interval [-2,2]. (20 points) Evaluate the integral. (5 points) (( VX - x ) ( = + 2 ) dxSolve the differential equation. (10 points) (212 + x2 ) dy + 2xydx = 0Evaluate the integral. (10 points) x 2 dx (9x2 - 4) 5/2Find the partial fraction decomposition for the expression. (10 points) 90 (2x - 1)(x + 2)(x2 + 2)Solve the differential equation. (10 points) y' + 2y = xSolve the initial value problem. (10 points) dy = (1 - x) cos y, y(4) = 0 dxAn object moves in one dimension with a velocity in m/s given by v(t) = 8 sin(nt) + 4t Find its average velocity over the time interval from t = 0 to t = 10, where t is measured in seconds. (5 points)