6.4_Fundamental_Theorem_of_Calculus_summer

6.4_Fundamental_Theorem_of_Calculus_summer - Evaluate the...

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6.4 The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus: Let f be continuous on [a,b]. Then a b f(x) dx = F(b) – F(a) where F is any antiderivative of f, that is F’(x) = f(x). Geometric Interpretation of a Definite Integral a b f(x) dx = F(b) – F(a) Represents the “signed area” between the graph of f(x) and the x axis on the interval [a,b] That is: the area above the x axis minus the area below the x axis on the interval [a,b]. Find the exact area under the graph of f(x) =10 - x 2 on [-1,2] (56/3) Find the area under the graph of f(x)= -1/3x + 1 on the interval [1,3] (2/3)
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Find the area under the graph of f(x)= 4x 2 + 6x + 10 on the interval [1,7] (660) Evaluate the definite integral 2 21 52 dx (988) Evaluate the definite integral 0 1 (x 6 – 2x 2 + 1)dx Give answer as fraction (10/21)
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Unformatted text preview: Evaluate the definite integral ∫ 2 (x – 4) (x - 1 )dx Give answer as fraction (2/3) A company produces chairs. Management has calculated that the marginal cost function for producing x chairs is C’(x) = .0015x 2- .04x + 11 dollars/unit and x denotes the number of units. Fixed costs are 700 per day. What is the total cost of producing the 111 st through 220 th units/day. 110 ∫ 220 C’(x) = 5143 to nearest integer Evaluate the definite integral 1 ∫ 2 (6/x )dx 6ln(2) The velocity of the Sea Falcon II t seconds after firing a booster rocket is v(t) = -t 2 + 20 t + 440ft/sec, 0< t< 20. Find the distance covered by the boat over the 10 second period after the booster was activated. ∫ 10 v(t) = 15200/3 Evaluate the definite integral 1 ∫ 3 e x dx e 3- e...
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This note was uploaded on 10/07/2011 for the course MATH 1431 taught by Professor Vaughn during the Spring '08 term at LSU.

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6.4_Fundamental_Theorem_of_Calculus_summer - Evaluate the...

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