(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) The variable h measures the distance from the right endpoint of the triangle to the slice. When h = 0 the slice is at the right tip of the triangle, and when h = 10 the slice is all the way on the left.
We will call the height of a slice y. We have similar triangles again. This means
The area of the slice at distance h from the right tip of the triangle is
The limits of integration are the values that make sense for h, which are 0 to 10, so the area of the triangle is