Mathematics

 Evaluate  : $$ \displaystyle \int _{ 10 }^{ 2 }{ { \left( { x }^{ 2 }+x+2 \right) dx } } $$


SOLUTION
$$\displaystyle \int_{10}^{2}{\left({x}^{2}+x+2\right)dx}$$
$$=\left[\dfrac{{x}^{3}}{3}+\dfrac{{x}^{2}}{2}+2x\right]_{10}^{2}$$
$$=\dfrac{1}{3}\left(1000-8\right)+\dfrac{1}{2}\left(100-4\right)+2\left(10-2\right)$$
$$=\dfrac{992}{3}+\dfrac{96}{2}+2\times 8$$
$$=\dfrac{992}{3}+48+16$$
$$=\dfrac{992}{3}+64$$
$$=\dfrac{1184}{3}$$
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Subjective Medium Published on 17th 09, 2020
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