Q. 2 TF - Calculus

Question

Functions defined by area accumulation: We know that for fixed real numbers a and b and an integrable function f, the definite integral ${\int }_a^{b}f\left(x\right) dx$is a real number. For different real values of b, we get (potentially) different values for the integral ${\int }_a^{b}f\left(x\right) dx.$

What is the word that describes the kind of relationship that exists between the values of b and the corresponding value of the integral?

Step-by-Step Solution

Answer

In the integral ${\int }_a^{b}f\left(x\right) dx,$a and b are the x values which are called limits of integration where b is the upper limit.

Step 1. Given information.

The given integral is ${\int }_a^{b}f\left(x\right) dx.$

Step 2. Explanation.

In the integral ${\int }_a^{b}f\left(x\right) dx,$ a and b are the x values which are called limits of integration where a is the lower limit and b is the upper limit.