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227wksht1

# 227wksht1 - g(2(c Explain how your answers to a relate to...

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Math 227.04 Integration Review Due in class Friday 1/28/11 Name Instructions. Please do your preliminary work on scratch paper. Write your °nal solutions in the space provided. You solutions should be written in complete English and mathematical sentences. Indicate your answers clearly. 1. Let f be the function whose graph is given below and suppose g is a function de°ned by g ( x ) = R x 0 f ( t ) dt: 3 2.5 2 1.5 1 0.5 0 2 1.5 1 0.5 0 x y (a) On the graph above, indicate geometrically the quatities: g (2 : 1) ° g (2) ; g (2 : 1) ° g (2) 0 : 1 ; f (2) : Supply clear labels. (b) Apply the Fundamental Theorem of Calculus to estimate

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Unformatted text preview: g (2) : (c) Explain how your answers to ( a ) relate to the answer in ( b ) : 1 2. Decide which of the following anti-derivative formulas are correct. In parts (a) and (b), if the formula is incorrect, determine the correct formula using the "guess and check" method. (a) Z cos(3 x ) dx = 3 sin (3 x ) + C: (b) Z e 3 x dx = e 3 x + C (c) Z e x 2 dx = e x 2 2 x + C 3. Evaluate (a) Z 2 ( p x + e 3 x ) dx (b) Z 2 1 ( 3 t & 1 t 2 ) dt 2...
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