Final answer:
Calculate the definite integral of y=x2+2x-3 between its roots, which are the points of intersection with the x-axis, to determine the area between the curve and the x-axis.
Step-by-step explanation:
The student is asking about the proper definite integral to find the area between the curve y=x2+2x-3 and the x-axis. To find this area, we need to determine the points where the curve intersects the x-axis, which are the roots of the equation x2+2x-3=0.
Once we have these points, which we can call x1 and x2, we can set up the definite integral from x1 to x2 of the function f(x). The integral calculates the sum of infinitesimally small areas under the curve, providing the total area between the curve and the x-axis.
To solve for the roots, we factor the quadratic equation: (x+3)(x-1)=0. So the roots are x1=-3 and x2=1. The definite integral of the function from x1 to x2 gives us the total area: \(\int_{-3}^{1} (x^2+2x-3) dx\).