Graph the integrand and use geometry to evaluate the integral

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Graph the integrand and use geometry to evaluate the integral.

$$\int_{-3}^{3}|x|+8\,dx$$

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2 Answers

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$3(11 + 8)/2$ area in the positive quadrant. Multiply by two for symmetry.

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$|x| + 8$ is a "v"-shaped graph, opening upwards, with its vertex at (0,8) and the sides of the "v" having slope 1 and -1. To evaluate the integral geometrically just draw the quadrilaterals formed by $(-3,11),(0,8),(0,0),(-3,0)$ and $(0,0),(0,8),(3,11),(3,0)$ and use conventional area formulas for rectangle and triangle to find the area bounded by the graph and the x-axis.

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