Evaluate the integral.
\[
\int_{3}^{5}(2 x+6) d x
\]

Answer

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Answer

So, the integral of the function from 3 to 5 is \(\boxed{28}\)

Steps

Step 1 ：Given the integral \(\int_{3}^{5}(2 x+6) d x\)

Step 2 ：Find the antiderivative of the function \(2x + 6\), which is \(x^2 + 6x\)

Step 3 ：Evaluate the antiderivative at 5, which gives \(5^2 + 6*5 = 55\)

Step 4 ：Evaluate the antiderivative at 3, which gives \(3^2 + 6*3 = 27\)

Step 5 ：Subtract the two results to get the final answer, \(55 - 27 = 28\)

Step 6 ：So, the integral of the function from 3 to 5 is \(\boxed{28}\)