Module 3

Module 3

1. 3.1 Antiderivative of an algebraic function

   • ∫f(u) du

2. 3.2 Antiderivative of a trignometric function

   • ∫cos x dx = sin x + C
   • ∫sin x dx = -cos x +C
   • sec^2 x dx = tan x + C
   • csc^2 x dx = -cot x + C
   • sec x tan x dx = sec x + C
   • csc x cot x dx = -csc x + C

3. 3.3 Antiderivative of an exponential function and logarithmic function

   • ∫tan x dx = -ln(cos x) + C
   • ∫cot x dx = ln(sin x) + C
   • ∫sec x dx = ln(sec x tan x) + C
   • ∫csc x dx = -ln(csc x cot x) + C

4. 3.4 Substitution rule review

   • Use of ∫f(u) du

5. 3.5 Indefinite integrals with given conditions

   • dy / dx
   • d^2y / dx^2
   • d^3y / dx^3

6. 3.6 Position, velocity and acceleration

   • f(t) = S = Position
   • f'(t) = V = Velocity
   • f''(t) = A = Acceleration

7. 3.7 Trigonometric integrals

   • sin^2 x = (1 - cos 2x) / 2
   • cos^2 x = (1 + cos 2x) / 2

8. 3.8 Trigonometric integrals

   • sin^2 x + cos^2 x = 1
   • tan^2 + 1 = sec^2 x
   • 1 + cot^2 = csc^2 x

9. 3.9 Application problems

10. 3.10 Properties of the definite integral

11. 3.11 The fundamental theorem of calculus

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