Mathematics

Solve the equation:-
$$\int_{0}^{2} [x^{2}-x+1]dx$$


SOLUTION
$$\displaystyle\int_{0}^{2}{\left({x}^{2}-x+1\right)dx}$$

$$=\left[\dfrac{{x}^{3}}{3}-\dfrac{{x}^{2}}{2}+x\right]_{0}^{2}$$

$$=\dfrac{1}{3}\left(8-0\right)-\dfrac{1}{2}\left(4-0\right)+\left(2-0\right)$$

$$=\dfrac{8}{3}-\dfrac{4}{2}+2$$

$$=\dfrac{8}{3}-2+2$$

$$=\dfrac{8}{3}$$

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Subjective Medium Published on 17th 09, 2020
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