Question

Determine the independent variable of the function$A\left(x\right)={\int }_a^{x}f\left(t\right)dt$

what the dependent variable represents and to explain for calling to be the dummy variable. In the above expression, x is the independent variable.

Short answer

A(x) depends on t so it is a dependent variable and it represents the signed area under

the graph of f(t) from t=0 to t= x.

Step-by-step solution

Step 1. Given information 

The given function is$A\left(x\right)={\int }_a^{x}f\left(t\right)dt$

Step 2. Calculation

Since, A(x) depends on t so it is a dependent variable and it represents the signed area under

the graph of f(t) from t=0 to t= x.

The term t does not appear on the output also it does not affects the dependent and independent variable and hence it is called the dummy variable.