I’m working on a Mathematics exercise and need support.

**Finish 6.4、6.5、7.1 by due time.**

What you should be able to do.

◦ for indefinite integrals

◦ for definite integrals

◦ changing limits of integration

◦ w.r.t. x

◦ w.r.t. y

◦ cross-sections (slicing)

◦ of revolution

∗ using washers/discs

∗ using cylindrical shells

◦ springs

◦ pumping

◦ R udv = uv − R vdu

◦ use of identities to evaluate

◦ know or be able to find quickly R tan x dx = ln |sec x| + c

◦ know R sec x dx = ln |sec x + tan x| + c

◦ integrals involving sinn x cosm x

◦ integrals involving tann x secm x