Learning Guide Learning Guide

84 • Chapter 3: Finding Solutions∫ π∫ π∫ π0 x cos(x) + x dx = 0 x cos(x) dx + 0 x dxUse the power rule.> Rule[power](%);∫ π0 x cos(x) + x dx = ∫ π0 x cos(x) dx + 1 2 π2Use the Hint command to determine a possible next step for theproblem.> Hint(%);[parts, x, sin(x)]Use the hint with the Rule command.> Rule[%](%%);∫ π0 x cos(x) + x dx = − ∫ π0 sin(x) dx + 1 2 π2Use the sin rule to complete this computation.> Rule[sin](%);∫ π0 x cos(x) + x dx = −2 + 1 2 π2Use the Student[Calculus1] package to calculate the limit of (1 +1/x) x .Use the Understand command to use rules for calculating the Limitwithout explicitly applying them. Understand the constant, constant multiple,power, and sum Limit rules for the following example.> Understand(Limit, constant, ‘c*‘, power, sum);Limit = [constant, constantmultiple, power, sum]