Find the area bound by the curve y=x^2-16 , the x-axis and the lines x=2 and x=5. i am trying to use the definite integral way ∫_2^5. but i am not getting the right answer. the right answer is 53/3
Draw a diagram. You will notice that part of the area you are trying to find is below the x-axis and part is above the x-axis. The graph cuts the x-axis between x=2 and x=5 (at x=4 to be precise).
In this case you need to find the integral from 2 to 4, which will be negative, so you need to find the absolute value to find the physical area. Then integrate from 4 to 5 (this will be positive reflecting the area above the x-axis). Then add the two areas together.