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• ## Discussion

 1 answerLast reply by: Lukasz SkoraWed Jan 18, 2012 9:41 AMPost by Romin Abdolahzadi on December 7, 2010[AT 48:37] If you do the integral of x^3 - the integral of x separately then you obtain a result of: (x^4/4 - x^2/2) + cProfessor Jishi, through u-substitution, obtained a result of: (x^2-1)^2/4 + cClearly we can see if we sub in a value of x=1 then we get completely different results; first one being -1/4 + C and second one giving 0 + C. Did Professor Jishi make a mistake? I keep looking at his u-substitution and it seems he does everything logically step-by-step.

### Integrals

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Definite Integrals 0:20
• F(x)
• Area
• Indefinite Integrals 13:53
• Suppose Function f(y)=∫f(y) dy
• g(x)=∫ f(x) dx
• ∫2 dx=2x+c
• Evaluation of Definite Integrals 25:20
• ∫f(x') dx'=g(x)
• Integral of Sin(x) ,Cos(x) , and Exp(x) 36:18
• ∫ sinx dx=-cos x+c
• ∫ cosx dx=sin x+c
• ∫ co2x dx=sin2x
• ∫Cosωdt=1/ωsin ωdt
• ∫e^x dx=e^x+c
• Integration by Substitution 45:23
• ∫x(x^2 -1)dx
• Integration by Parts 52:30
• d/dx=(uv)'
• ∫udv=∫d(uv)-∫Vdu =uv-∫vdu
• ∫xe^x dx/dv
• Extra Example 1: Integral
• Extra Example 2: Integral