# Thread: Final exam tomorrow, need help!

1. ## Final exam tomorrow, need help!

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

2. Have you made any attempts at these or are we working with a blank canvas? Showing some working will help us help you.

Originally Posted by DanS29
a) Initial value problem
dy/dx=y^2 + 1
y(4)=0
This first one is separable.

$\displaystyle \frac{dy}{dx}= y^2 + 1$

$\displaystyle \frac{dy}{ y^2 + 1}= dx$

Now integrate both sides, after you show me that, I will show you more.

3. a
y=tan(x-4)

d
$\displaystyle y=\pm\frac{1}{7}\sqrt{35x^2+49C}$

4. 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
Damn! thats too many questions... it is hard to read.. it would be great if you posted the questions separately

for no.c to find the length of the curve:

first find out the derivative of the given funciton...and then the length of the curve is given by

$\displaystyle L =\int_1^2 \sqrt {1+ \mbox{(derivative)}^2} \mbox{dy}$

you can check your answers for differentiation, integration etc. at this website