Question: 4. HOMEWORK In each integration problem sketch for yourself a corresponding graph to ensure that your answer is reasonable. (1) Evaluate the area under the

4. HOMEWORK In each integration problem sketch for yourself a corresponding graph to ensure that your answer is reasonable. (1) Evaluate the area under the graph of y = 3-2 above the X-axis between = 27 and x= 81? (2) Evaluate the definite integral fc, |a|da. (3) Evaluate the definite integral f +" dr. (4) (a) Find the average value of cost on the intervals [0,7], [0,7/2].[0,/4],[0,0.01]. (b) Determine the general formula for F to,2] the average of cost over the interval {0, x]. (c) Calculate lim,_,o Ft0,2)- (5) Evaluate the definite intergral [7 (sec? x + 3x)dz. (6) Evaluate [ | cos s|ds. (7) Find the general antiderivative [ ~?/*dz. Then verify by differentiation that your answer is correct. (8) Let 2 ift 1 Sketch by hand a graph of y = f(t). Let g(x) = [", f(t)dt be defined for -2

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