Mathematics

Evaluate the following definite integrals as limit of sums.
$$\displaystyle\int^b_axdx$$.


ANSWER

$$\dfrac{b^{2}-a^2}{2}$$


SOLUTION
$$=\int_{a}^{b} x dx$$

$$=\int_{a}^{b} \dfrac{x^2}{2}$$

$$=\dfrac{b^2-a^2}{2}$$ Ans.

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