One of the great advances of classical geometry was obtaining formulas to determine the area and volume of triangles, spheres, and cones. However, ...

One of the great advances of classical geometry was obtaining formulas to determine the area and volume of triangles, spheres, and cones. However, there is a method for calculating the areas and volumes of more general shapes. This is called an integral, a tool for calculating much more than areas and volumes, of fundamental importance in science and engineering. It allows us to calculate quantities ranging from probabilities to averages to energy consumption and forces acting against the gates of a dam. We will study a variety of these applications in the next chapter, but we will focus on the concept of the integral in its use in calculating various regions with curved contours. Considering your knowledge of integrals and their relationship with curve areas, judge the statements below as (V) True or (F) False.

It can be used to calculate the area of the region bounded by the function f(x) and the vertical lines x=a and x=b.
The area bounded above by the curve f(x) and below by the curve g(x) and bounded by the lines x=a and x=b can be calculated.
The only application for integrals in engineering is the calculation of the area below a curve between two points.
When we calculate f(x)dx of a continuous function, we are calculating a value that represents the total length of the arc of that curve from a to b.
a) V-V-V V-F-V-F
b)
c) V-V-F-V
d)
e) F-V-V-F