Question: 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

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 = V3 . x above the X-axis between x = 27 and x = 81? (2) Evaluate the definite integral S, ladxc. (3) Evaluate the definite integral Sy act 2 2 dac.(4) (a) Find the average value of cost on the intervals [0,7], [0,7/2],[0,7/4],[0,0.01]. (b) Determine the general formula for f{o,.) the average of cost over the interval [0, x]. (c) Calculate lim,_,9 Fo , (5) Evaluate the definite intergral fy 3 (sec? a + 3x)dz. (6) Evaluate > | cos s|ds. (7) Find the general antiderivative f 2~?/*dz. Then verify by differentiation that your answer is correct. (8) Let 2 ift1 Sketch by hand a graph of y = f(t). Let g(x) = f(t)dt be defined for 2

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