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.

  • Substitution Rule
  • ◦ for indefinite integrals

    ◦ for definite integrals

    ◦ changing limits of integration

  • integrals involving symmetric functions
  • area between curves
  • ◦ w.r.t. x

    ◦ w.r.t. y

  • volumes
  • ◦ cross-sections (slicing)

    ◦ of revolution

    ∗ using washers/discs

    ∗ using cylindrical shells

  • work
  • ◦ springs

    ◦ pumping

  • average value of a function on an interval
  • Mean Value Theorem for Integrals
  • integration by parts
  • ◦ R udv = uv − R vdu

  • trigonometric integrals
  • ◦ 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