I need help on how to use the definite integral to find area within a closed interval

Question

When I'm given a function like f(x)=e^x-2 and a closed interval of something like [-1,5] I don't think I'm using the function in my calculator correctly and I think I've confused myself on how to do it by hand. Please help!

Answer 1

When using definite integrals to find the area under the curve be sure to use the absolute value for the portion of the curve below the x axis. You can do this by separating the integral into intervals. In your case, your integral will be -f(x) over the interval [-1, solve for x where e^x-2=0] and f(x) over the interval [solve for x where e^x-2=0, 5]. Please feel free to contact me if you need further explanation.