the integral gives the area under the curve, that is, the area between the curve and the x-axis. if the curve is below the x-axis, the integral gives the negative area. with that in mind, you should be able to follow this easily Originally Posted by
mathaction You are given the graph below where
A1 =
18 and A2 = 5. (The graph is not drawn to scale.)
Figure 5.29
Use Figure 5.29 to find the following values.
(a)
=
$\displaystyle \int_a^b f(x)~dx = A_1$
(b)
=
$\displaystyle \int_b^c f(x)~dx = - A_2$
(c)
=
$\displaystyle \int_a^c f(x)~dx = \int_a^b f(x)~dx + \int_b^c f(x)~dx$
(d)
=
$\displaystyle \int_a^c f(x) = A_1 + A_2$ (the absolute values flips the negative part of the graph up, so now the area for the second part is positive when given by the integral)