AP Calc: use geom formulas to find integral of piecewise fcn

[venialove]

let f(x)= {3, x ? 3
{6, x > 6
Use the geometric formulas to find ? f(x) dx
1

 

[venialove]

Re: math (piece-wise function)

This is the integral

6
?f(x) dx
1

 

[pka]

Re: math (piece-wise function)

I think you mean \(\displaystyle f(x) = \left\{ \begin{array}{l} 3,\,\,x \le 3 \\ 6,\,\,x > 3 \\ \end{array} \right.\)

Then \(\displaystyle \int\limits_0^6 {f(x)} = \int\limits_0^3 {f(x)} + \int\limits_3^6 {f(x)} = \int\limits_0^3 {3dx} + \int\limits_3^6 {6dx}\).

 

[venialove]

Re: math (piece-wise function)

I'm sorry it's this
{3, x is less than or equal to 3
{6-x, x > 3

 

[pka]

Re: math (piece-wise function)

Well O.K.
Look at the last two integrals.
They represent the area of two rectangles.