We slice the region into horizontal strips of width Δ *y*. When we look at the horizontal strip at height *y*, the strip lies between two points, each with *y* as its second coordinate: The left endpoint of this strip is on the graph of the line *y* = *x*, so its full coordinates are (*x*,*y*) = (*y*,*y*). The right endpoint of the strip is on the graph of the curve *y* = *x*^{2}. If *y* = *x*^{2} then , so the full coordinates of the right endpoint are . The length of the strip is approximately : The area of the strip is approximately If we sum up the approximate areas of the strips and take the limit as the number of strips goes to ∞, we find that the area of the entire region is Thankfully, this also equals |