Evaluate the integral by interpreting it in terms of areas. In various other words, draw a snapshot of the area the integral represents, and also discover the location making use of high school geometry.

You are watching: Evaluate the integral by interpreting it in terms of areas.

∫9 to 0 of |9x−8|dx=

Giulia

If you graph this in Desmos or on a graphing calculator you will certainly watch the crucial points.

Touches the x axis when 9x - 8 = 0, ie x = 8/9

When x = 0, y = 8.

So you have the right to split the integral into 2 areas. From x = 0 to x = 8/9, will be the location of a appropriate triangle

base 8/9, elevation 8.

From x = 8/9 to x = 9, will certainly be the location of a right triangle. Base ( 9 - 8/9). When x = 9, y = 73 so height will be 73.

Find the areas of these two ideal triangles and also add together to acquire your answer.

Mike

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