Surface area of revolution

[Mathio]

I need help with this specific problem:
y = (1/4)x^4+(1/8)x^2, 1 ≤ x ≤ 2 rotated about y-axis. Compute the surface area.

I've done the work but I can't seem to integrate the problem to get the surface area. I can't figure out anyway to integrate this integration.

pi/2 ∫ x (sqrt(16x^6+8x^4+x^2+16))dx

This is what I am left with and I think there is no way to integrate this unless I am wrong.

 

[Mathio]

Can anyone help?

 

[tkhunny]

I need help with this specific problem:
y = (1/4)x^4+(1/8)x^2, 1 ≤ x ≤ 2 rotated about y-axis. Compute the surface area.

I've done the work but I can't seem to integrate the problem to get the surface area. I can't figure out anyway to integrate this integration.

pi/2 ∫ x (sqrt(16x^6+8x^4+x^2+16))dx

This is what I am left with and I think there is no way to integrate this unless I am wrong.

View attachment 11403

If it exists, there is never "no way". However, I don't have any good news or fancy tricks. You'll have to resort to numerical methods.

 

[Steven G]

1st please use equal signs!
Did you try to factor?
Did you try to complete the square?
Are you allowed to approximate the answer?

 

[Dr.Peterson]

Have you tried Wolfram Alpha? It gives a horrible indefinite integral, and a nice numerical value for the definite integral. This validates what has been said.

What is the context of the question? Do you have reason to think it was meant to be manually solvable? If so, have you checked that you copied correctly?