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Section 15-4 The Fundamental Theorem of Calculus If F(x) is the antiderivative of the continuous function f(x), then z b a f ( x ) dx = F(b) – F(a) Evaluate z 5 4 x 6 dx 5 1 5 Solution: F(x) = x + C F(b) – F(a) = 1 5 5 (5) - 1 5 5 (-6) = 10901/5 Evaluate each indefinite integral. z z 5 3x dx 1 2 Answer +c 2 3 4 x 6 (3x + 5x + 3x +2x +1) dx Answer: 3 5 5 x + 5 4 4 3 2 x +x+x +x+C What if you were asked to find the area enclosed by two figures? 2 Example: y= x +11 (this is a line) and y=(x-4) + 3 (this is a parabola). First graph them to get a visual. We solve the system of equations and see that 1 2 they intersect at (1,12) and (8,19). (8,19) z 8 x 11 - ((x-4) +3 dx = 1 (1,12) z 8 = 343/6 units 2 2 1 2 9 x -x -8 dx = 9 2 2 x - 1 3 3 x -8x Section 15.4 Pg 973 # 15-43 odd: Area worksheet