Use geometry to evaluate the integral from 0 to 10 of the function f of x, dx for f of x equals 5 for x less than or equal to 5 and equals the quantity 10 minus x for x greater than 5 .

Question

Use geometry to evaluate  the integral from 0 to 10 of the function f of x, dx  for  f of x equals 5 for x less than or equal to 5 and equals the quantity 10 minus x for x greater than 5 .

anonymous · Answer

$$f(x)=\begin{cases}5&\text{for }x\le5\10-x&\text{for }x>5\end{cases}$$
Consider the plot of the function:
|dw:1422465184204:dw|
Basically, the integral gives the area of the shaded figure above, which is a trapezoid. Find the dimensions of the trapezoid and compute the area.