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Question

Evaluate : $$\displaystyle \int _0^2 \dfrac x 3  dx $$


Solution


$$\displaystyle \int _0^2 \dfrac x 3  dx $$

we know that $$\displaystyle\int{{x}^{n}dx}=\dfrac{{x}^{n+1}}{n+1}+c$$

$$=\dfrac 13 \left. \dfrac {x^2}2\right]_0^2$$ 

$$=\dfrac 46-0$$

$$=\dfrac 23$$


Mathematics

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