Integration Exercises
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Exercises from public domain textbooks. Solutions where provided do not necessary follow the same lines as the original.

Solutions are not given for exercises whose number is not linked

Some exercises which do not have a textbook solutions are worked: beware of errors.

Evaluate the integral. Check by differentiation.

D80-1a. {$\displaystyle \int x^3 dx $}

worked

D80-1b. {$\displaystyle \int (2x - x^2) dx $}

worked

D80-1c. {$\displaystyle \int (1-4t^4) dt $}

worked

D80-1d. {$\displaystyle \int (1 + y^2) dy $}

worked

D80-1e. {$\displaystyle \int {{dx} \over {x^2}} $}

worked

D80-1f. {$\displaystyle \int (\sqrt x - {2 \over {\sqrt x}}) dx $}

worked

D80-2. {$\displaystyle \int {{dx} \over x} $}

worked

C98-1. {$\displaystyle \int (1-x)(1+x^2)dx $}

worked

C98-2. {$\displaystyle \int {{1+2x+3x^2} \over x^3}dx $}

worked

C98-3. {$\displaystyle \int (a+bx)^2 dx $}

worked

C98-4. {$\displaystyle \int {{(3x-2)^2} \over x^2} dx $}

worked

C98-5. {$\displaystyle \int (e^x - e^{-x})^2dx $}

worked

C98-6. {$\displaystyle \int {{x^{3 \over 2} -4x^{1 \over 3}} \over x}dx $}

worked

C98-7. {$\displaystyle \int (1-2x)^2\sqrt x dx $}

worked

C98-8. {$\displaystyle \int (x^3 - 2)(x^{1 \over 2} + x^{2 \over 3}) dx $}

worked

D80-3. {$\displaystyle \int \sin\theta d\theta $}

D80-4. {$\displaystyle \int \sin 2\theta d\theta $}

D80-5. {$\displaystyle \int \sqrt{x+1} dx $}

D80-6. {$\displaystyle \int \sqrt{1-x} dx $}

D80-7. {$\displaystyle \int e^{2x} dx $}

D80-8. {$\displaystyle \int (1+2x)^3 dx $}

D80-9. {$\displaystyle \int x\sqrt{a^2 + x^2} dx $}


Sources:

  1. Elements of the Differential and Integral Calculus Wikisource
  2. Calculus Made Easy by Silvanus P. Thompson Project Gutenberg
  3. Davis,Ellery Williams, William Charles Brenke, Earle Raymond Hedrick. The Calculus (Macmillan Company, 1922) Google Books
  4. Love, Clyde E., Earl David Rainville Differential and Integral Calculus (Macmillian, 1916) Google Books

Recommended:

Category: Math Calculus Integration


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