# How do you evaluate the definite integral #int (2+x)dx# from [0,4]?

## 16

applying the rule of power

we have

There's no need for the limited constant.

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To evaluate the definite integral (\int_{0}^{4} (2+x) , dx), you can follow these steps:

- Find the antiderivative of the integrand (2+x) with respect to (x), which is (2x + \frac{1}{2}x^2).
- Evaluate the antiderivative at the upper limit of integration (4) and subtract the value of the antiderivative at the lower limit of integration (0).

[ \int_{0}^{4} (2+x) , dx = \left[2x + \frac{1}{2}x^2\right]_{0}^{4} = \left(2(4) + \frac{1}{2}(4)^2\right) - \left(2(0) + \frac{1}{2}(0)^2\right) ] [ = (8 + 8) - (0 + 0) = 16 ]

Therefore, the value of the definite integral is 16.

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