Please find the area bounded by the curves f(x)=-cos(x) and g(x)=-x^2+5. (Please set up the integral. You may use NINT to compute)
The first thing you should do is graph both curves to get an idea of what the area looks like and where the curves are compared to each other.
The first thing you should do is graph both curves to get an idea of what the area looks like and where the curves are compared to each other.
The less bold line is f(x) and the bolder line is g(x). As you see, g(x) is above f(x) and so the integral should be g(x)-f(x). To find the bounds, you find where the curves intersect and use the x-value. These values are -2.1 and 2.1. We have our bounds and we have what is in the integral, so let's put everything together. The final product should look like this:
After you find the integral, you type in all the information into NINT like so: (-x^2+5)-(-cos(x)),x,-2.1,2.1 and the calculator spits the answer.