Graph the function G of X equals the absolute value of X + 5 and find its average value over the following intervals. Well, the absolute value of X has a definition. If it's X is greater than or equal to 0, it's just X. But if X is less than 0, it's the opposite of X or negative X. So G of X we could think of as X + 5 for X greater than or equal to 0 and negative X + 5 for X less than 0. Now, if we're trying to find the average, the average of the function G is going to equal 1 / b -, a on the integral of A to B of the function, the absolute value of X + 5 DX. So when we want -5 to five, we're going to look at that in -5 to 0 and then zero to 5 S 1 divided by our B minus a 5 - -5 and I have to split the function up into the two parts. So when we're at -5 to 0, we're going to have negative X + 5 DX. And then we're going to add that result to the average again, 1 minus 1 divided by the b -, a one over 5 - -5 for the zero to five, zero to five of the X + 5 DX. When we evaluate that and simplify, we end up with 15 halves. So we take the anti derivative and we substitute in the upper bound minus the lower bound. On the next interval, five to seven, we're actually only going to use the X + 5 portion. So if we look at this one on five to seven, once again having our function here, G of ** +5, when X is greater than or equal to 05 to seven, that whole thing's greater than or equal to 0. So 1 divided by the 7 -, 5, the integral five to seven of X + 5 DX. Evaluate that, put in our upper bound minus our lower bound, and we could come up with 11 from -5 to seven. We're going to have to split it up into two parts again, because part of it's less than 0 and the other parts greater than 0. So 1 / 7 - -5 from -5 to 7 is really the absolute value of X + 5 DX. So we're going to split that up into two cases, 112th -5 to 0 using the portion for when X was less than 0, and then plus 112th zero to seven using the portion when X is greater than or equal to 0. When we evaluate that, we put in our upper bound minus our lower bound and then we add the second piece, our upper bound minus our lower bound times that 112th in front and we get 97 twelfths.