5.1 Antidifferentiation--Indefinite Integral

5.1 Antidifferentiation--Indefinite Integral - -= âˆ âˆ âˆ...

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MAC2233 (3.4) FIU, MDC- North 5.1 Antidifferentiation: The Indefinite Integral A function F(x) is said to be an  antiderivative  of f(x) if F’(x) = f(x) for every  x  in the domain of f(x).  In other words, you are  taking a derivative and finding the function from which it came.  Since, for the derivative of a function,  all constants in the  function equal zero, when finding the function from the derivative, the constant could be any constant C.  Thus, the indefinite  integral of a function has the form f(x) + C.   Constant Rule:    k dx kx C = +  for constant  k .   Power Rule:  n n x x dx C n 1 1 + = + + , n ≠ -1.   Logarithmic Rule:    dx x C x 1 ln = + x ≠ 0 .   Exponential Rule:  kx x e dx e C k 1 = + k ≠ 0 .   Constant Multiple Rule:   kf x dx k f x dx ( ) ( ) = ∫ ∫  for constant  k .   Sum Rule:  ( 29 f x g x dx f x dx g x dx ( ) ( ) ( ) + = + ∫ ∫ ∫ .   Difference Rule:   ( 29 f x g x dx f x dx g x dx ( )

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Unformatted text preview: ( ) ( ) -=- âˆ« âˆ« âˆ« . Find the indicated integral. Check your answers by differentiation. 1. x dx 0.3-âˆ« 2. dy y y y 2 1 2 3 2 -+ Ã· Ã· âˆ« 3. x x dx x 2 3 2 +- Ã· âˆ« 4. ( 29 t t e e dt 0.02 0.13 4--+ âˆ« MAC2233 (3.4) FIU, MDC-North 5. If dy x dx x 1 + = , find y = f(x) where y = 5 when x = 4. #34 6. If ( 29 f x x x 1 2 '-= + is the slope of the tangent line at each point (x, y) on the curve y = f(x) and the curve contains the point (1, 2), find f(x). #38 7. The marginal revenue derived from derived from producing q units of a certain commodity is Râ€™(q) = 4q â€“ 1.2q 2 dollars per unit. If the revenue derived from producing 20 units is \$30,000, how much revenue should be expected from producing 40 units?...
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5.1 Antidifferentiation--Indefinite Integral - -= âˆ âˆ âˆ...

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