How do you find the integral of #x^2-6x+5# from the interval [0,3]?

1 Answer
May 13, 2018




We can use the reverse power rule:

#f(x) = x^2 -6x + 5x^0#


#int_0^3x^2 - 6x + 5x^0dx = [x^3/3-6x^2/2+5x^1/1]_0^3#

This is equivalent to:


Therefore, the answer is -3. Note that the definite integral gives the net area under the graph. The negative sign implies that there is more area below the x-axis (than above) for the interval from 0 to 3 (inclusive).

If you are unfamiliar with the reverse power rule, this might help: