Mathematics

$$\int^{4}_{1}\left(x^{2}-x\right)dx$$


SOLUTION
$$\int_{1} ^{4}(x^2 - x)dx = \left[\dfrac{x^3}{3} - \dfrac{x^2}{2} \right]_{1} ^{4}$$

$$= \left(\dfrac{4^3}{3} - \dfrac{4^2}{2} \right) - \left( \dfrac{1^3}{3} - \dfrac{1^2}{2} \right) $$

$$= \left(\dfrac{64}{3} - \dfrac{16}{2} \right) - \left( \dfrac{1}{3} - \dfrac{1}{2} \right) $$

$$= \dfrac{40}{3} - \dfrac{1}{6} $$

$$= \dfrac{79}{6} $$ (Ans)
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Subjective Medium Published on 17th 09, 2020
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