Can you evaluate the integral by interpreting it in terms of areas?

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Answer 1 · 2018-05-28T16:45:14

#int_(-4)^3 1 -xdx = 21/2#

Let's sketch the graph of #f(x) = 1 - x#. Add the vertical lines #x =-4# and #x = 3#.

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Integrating is just finding the area under a curve, so since we have two triangle, we just find their areas, add them up and we're all done.

The first triangle has base length of #5# units and height #5# units. The area is therefore #(5 * 5)/2 = 25/2#.

The second triangle has base length #2# and height #-2#. Therefore the area will be #(2 * -2)/2 = -2#

Therefore #int_(-4)^3 1 - x dx = 25/2 + (-2) = 21/2#

Hopefully this helps!