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 .
12.5
25
37.5
Cannot be found
4 answers
c'mon - did you draw the figure? It's just a trapezoid, with height 5 and bases 5 and 10.
Steve you are an !@#$%^&
Answer is 37.5
It is 37.5.
The geometric representation of an integral is the area below the curve. So, let's graphic the function.
F(x) = 5 is an horizontal line, (y = 5)
and f(x)=10-x is also a line, but it is decreasing.
If you graph this out, you can see in the image that the area below the curve happens to be a polygon. In order to calculate the area we are going to separate it into simpler polygons: a square and a triangle.
The area of the square is 5 times 5 = 25.
The area of the triangle is 5 times 5 divided by 2 = 12.5.
If we add them, we get the integral from 0 to 10 of the function f of x, dx = 25 + 12.5 = 37.5
The geometric representation of an integral is the area below the curve. So, let's graphic the function.
F(x) = 5 is an horizontal line, (y = 5)
and f(x)=10-x is also a line, but it is decreasing.
If you graph this out, you can see in the image that the area below the curve happens to be a polygon. In order to calculate the area we are going to separate it into simpler polygons: a square and a triangle.
The area of the square is 5 times 5 = 25.
The area of the triangle is 5 times 5 divided by 2 = 12.5.
If we add them, we get the integral from 0 to 10 of the function f of x, dx = 25 + 12.5 = 37.5