Evaluate the following definite integrals as limit of sums.
$\int_{a}^{b} x d x$ .

b^{2} + a^{2}

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\frac{b^{2} - a^{2}}{2}

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a^{2} - b^{2}

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a^{2} + b^{2}

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Solution

The correct option is C $\frac{b^{2} - a^{2}}{2}$
$= \int_{a}^{b} x d x$

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

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

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