(a) Find an integral expression for the area of the triangle using the slice and variable of integration indicated.
(b) Evaluate your integral and check that it agrees with the area you find using the formula
(a) Now the variable h measures the distance from the left end of the triangle to the slice. When h = 0 the slice is at the left end; when h = 12 the slice is at the right tip.
Let the height of the slice at position h be called y. To find y we can use similar triangles as we did in the previous two problems. However, the base of the smaller triangle is not h. The base of the smaller triangle is now 12 – h. Using similar triangles, we have