## Quick Reference

Let *y*=*f*(*x*) be the graph of a function *f* such that *f*′ is continuous on [*a*, *b*] and *f*(*x*)≥0 for all *x* in [*a*, *b*]. The area of the surface obtained by rotating, through one revolution about the *x*-axis, the arc of the curve *y*=*f*(*x*) between *x*=*a* and *x*=*b*, equals

Parametric form

For the curve *x*=*x*(*t*), *y*=*y*(*t*) (*t* ∈ [*α*, *β*]), the surface area equals

Polar form

For the curve *r*=*r*(*θ*) (*α*≤*θ*≤*β*), the surface area equals

*Subjects:*
Mathematics.

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