Calculus/Integration/Exercises

From Wikibooks, the open-content textbooks collection

Jump to: navigation, search
← Improper integrals Calculus Area →
Integration/Exercises

Contents

[edit] Set One: Sums

[Insert Numbered Problems Here]

Solutions to Set One

[edit] Set Two: Integration of Polynomials

Given the above rules, practice indefinite integration on the following:

  1. \int x^{12}\, dx
  2. \int 8x^3\, dx
  3. \int 4x^2+11x^3\, dx
  4. \int 31x^{32}+4x^3-9x^4 \,dx
  5. \int 5x^{-2}\, dx

Solutions to Set Two

[edit] Indefinite Integration

Antiderivatives

  1. \int \cos x+\sin x\, dx
  2. \int 3\sin x\, dx
  3. \int 1+\tan^2 x\, dx
  4. \int 3x-\sec^2 x\, dx
  5. \int -e^x\, dx
  6. \int 8e^x\, dx
  7. \int \frac1{7x}\, dx
  8. \int \frac1{x^2+a^2}\, dx

[edit] Integration by parts

  1. Consider the integral \int \sin(x) \cos(x)\,dx. Find the integral in two different ways. (a) Integrate by parts with u = sin(x) and v' = cos(x). (b) Integrate by parts with u = cos(x) and v' = sin(x).

Compare your answers. Are they the same?


Solutions to Set Three

Navigation: Main Page · Precalculus · Limits · Differentiation · Integration · Parametric and Polar Equations · Sequences and Series · Vector Calculations · Multivariable Calculus & Differential Equations · Extensions · References

Retrieved from "http://en.wikibooks.org/wiki/Calculus/Integration/Exercises"