Question

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

Answer 1

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

Explanation:

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

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!