$\int_{0.2}^{3.5} x \, dx$ is equal to - DASH

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$\int_{0.2}^{3.5} x \, dx$ is equal to

4

4.5

3.5

3

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Step 1: Find the Indefinite IntegralThe indefinite integral of $x$ is given by: $ \int x \, dx = \frac{x^2}{2} + C $ Step 2: Evaluate the Definite IntegralWe need to evaluate the definite integral from 0.2 to 3.5: $ \int_{0.2}^{3.5} x \, dx = \left[ \frac{x^2}{2} \right]_{0.2}^{3.5} $ Step 3: Substitute the LimitsSubstitute the upper and lower limits: $ \left[ \frac{(3.5)^2}{2} \right] - \left[ \frac{(0.2)^2}{2} \right] $ Step 4: Calculate the ResultCalculate each term: $ \frac{(3.5)^2}{2} = \frac{12.25}{2} = 6.125 $ $ \frac{(0.2)^2}{2} = \frac{0.04}{2} = 0.02 $Subtract the results: $6.125 - 0.02 = 6.105$Therefore, the integral $ \int_{0.2}^{3.5} x \, dx $ is approximately 6.105, which is closest to option 2: 4.5.

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