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5.3.7-eg-1 - Example Evaluate the definite integral 3 2x...

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Unformatted text preview: Example Evaluate the definite integral 3 2x dx 0 by interpreting it as an area of a particular region. Solution: The integrand is 2x, and since the line y = 2x does not go below the x-axis for 0 ≤ x ≤ 3, this definite integrand can be interpreted as the area under the line y = 2x and above the x-axis, and between the vertical lines x = 0 and x = 3. The region is a right triangle with height h given by the height of the line y = 2x at the right endpoint x = 3, i.e., h = 2 · 3, and with base b given by the length of the integration interval, or b = 3 − 0 = 3. So the area is 1 1 bh = 3 · 6 = 9 2 2 square units. It follows that 3 2x dx = 9. 0 ...
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