Mathematics

Evaluate $$\displaystyle \int _{1}^{3}(x^{2}+3x+e^{x})dx$$, as the limit of the sum.


SOLUTION
Let $$ I = \int_{1}^{3} x^{2}+3x+e^{x}dx $$
$$ \Rightarrow I =  \int_{1}^{3} x^{2}dx+3 \int_{1}^{3}xdx+ \int_{1}^{3}e^{x}dx $$
$$ = \frac{x^{3}}{3} |_{1}^{3} +3\frac{x^{2}}{2} |_{1}^{3}+e^{x} |_{1}^{3} = \frac{27-1}{3}+\frac{3}{2}(9-1)+e^{3}-e $$
$$ I = \frac{26}{3}+12+e^{3}-e $$
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Subjective Medium Published on 17th 09, 2020
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