### Home > PC > Chapter 2 > Lesson 2.3.5 > Problem 2-130

Suppose we want to find the area under the curve

*f*(*x*) over the interval 1 ≤*x*≤ 10 using 25 sub-intervals. What is the width of each rectangle? Homework Help ✎What will the height of the first rectangle be if we use left-endpoint rectangles?

What will be the height of the first rectangle if we use right-endpoint rectangles?

What will be the height of the last rectangle if we use right-endpoint rectangles?

What will be the height of the last rectangle if we use left-endpoint rectangles?

How would your answers change if the interval were

*B*≤*x*≤*E*and the width of each rectangle were*W*?

*x*_{0} = 1 → height of rectangle = *f*(1)

Height of *x*_{1}.

For right-endpoint, we start at *x*_{1} and go to the end. So you want the height at that *x*_{end}.

For left-endpoint, we start at *x*_{0} and go to the *x*_{end-1}. So you want the height − *f*(end − width).

*x*_{0} = *B*→height of rectangle = *f*(*B*)*x*_{1} = *B* + width →height of rectangle = *f*(*B* + width)*x*_{last} = *E* →height of rectangle = *f*(*E*)*x*_{OneBeforeLast} = *E*−width →height of rectangle = *f*(*E* − width)