Calculate the value of the definite integral (x^3 + 3x + 2) with limits x=2 and x=1
a) Integrate the given expression using integration laws we have learnt to give [(x^4)/4 + (3(x^2))/2 + 2x ] and you do not need a +c constant as we have limits.b) Substitute the limits into the equation we calculated remembering to do the upper limit substitution minus the lower limit substitution to give: [(2^4)/4 + (3)(2^2)/2 + 2(2)] - [(1^4)/4 + (3)(1^2)/2 + 2(1)] which equals [16/4 + 6 + 4] - [1/4 + 3/2 + 2]= [14] - [1/4 + 6/4 + 8/4] =[56/4] - [15/4]= 41/4
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