The equations are and on .
If the curve given by the parametric equations and on is rotated about the -axis, where are continuous and , then the surface area is .
Consider .
Apply derivative on each side with respect to .
.
Consider .
Apply derivative on each side with respect to .
.
Surface area is .
Substitute , and .
Substitute .
.
Consider .
Apply parts of integration formula: .
Consider .
.
Consider .
.
.
.
Substitute in .
.
.
"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!" June Barnett |
"Your site is amazing! It helped me get through Algebra." Charles |
"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful." Dan Pease |