Originally Posted by

**DanS29** I don't need any work shown I just need the answers so I can check my answer. I have my final exam tomorrow so I need to be sure I'm doing these right.

Any answer would help me out a lot, but the more I can get answers to the better.

Thanks so much!

a) Initial value problem

dy/dx=y^2 + 1

y(4)=0

b)Find the area of the surface obtained by rotating the curve about the y-axis?

y=(1/4)*x^2 - (1/2)*ln(x); 1≤x≤2

c)Find the length of the curve

x=((y^4)/8) + (1/(4*y^2)); 1≤y≤2

d)Solve the differential equation.

7yy' = 5x

e)Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the given axis.

y=e^x; 1≤y≤3; y-axis

f) Find the area of the surface obtained by rotating the curve about the x-axis.

x= (1/3)*(y^2 +2)^(3/2)

1≤y≤3

g)Find the area of the surface obtained by rotating the curve about the x-axis.

y=x^3

0≤x≤3