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PROBLEM 4 Use the limit definition of definite integral to evaluate . SOLUTION Divide the interval for into equal parts each of length . Choose the sampling points to be the right-hand endpoints of the subintervals and given by for . The function is . Then the definite integral is (Use summation rule 6 from the beginning of this section.) (Use summation rules 5 and 1 from the beginning of this section.) (Use summation rule 2 from the beginning of this section.) .