3.[4] Find the resulting surface area when y = ex, x > 0, is rotated about the x-axis. 4. [6] The density function, f(x) = = e3-x (1+e3-x)2 , is an example of a logistic distribution. (a) [4] Verify that f is a probability density function. (b) [2] Find P(3 X 4) 5.[3] Solve the differential equation: x + 3yx + 1 dy = 0, y(0) = 1 dx 6.[3] Solve the differential equation, xy' = y + xey/x by making the change of variable v=y/x. 7.[3] An integral equation is an equation that contains an unknown function y(x) and an integral that involves y(x). Find the solution of the following integral equation 1 y(x) = 2+ dt, x>0 ty(t)