Question

The total area bounded by the graph of the function y=f(x) and the x-axis from x=a to x=b is the area below the graph of y=|f(x)| from x=a to x=b. Find the total area bounded by the graph of f(x)=sin x and the x-axis from x=0 to x =2π

Solution

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For this activity, we will use a graphing calculator. We need to find the area bounded by f(x)=sinxf(x)=|\sin x| and the xx-axis from x=0x=0 to x=2πx=2\pi.

On a TI-83 Plus calculator (which I used), press MATH\textbf{MATH} then select fnInt(\textbf{fnInt(}. Enter the function, the variable, the lower limit, and the upper limit of the integral. The numerical integral of the function (and the required area) is:

=4\color{#c34632}=4

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