In this tutorial we'll be looking at finding definite integrals and finding the area under a graph. In run mode, you can type in a definite integral. In graph mode, you can not only evaluate the area but see it on the graph. To work along with this tutorial, you may find it easiest to reset your calculator before starting so that your screen matches the one in the video.
In run mode, use the math menu on the second page for the integral. Type the function and scroll to the right to type the limits. Execute and a fractional answer is given here. To see the area given by this integral, go to graph mode. Type in the equation, use the x theta t key for x and then draw.
Choose G-Solve and then the arrow for the second page of tools. Choose the first option for integral. Type the lower and the upper limits. Notice the decimal value of the integral is given. Its negative and the region that corresponds to it is shaded on the graph.
You can also find the area of the finite region between the curve and the x axis without having to find the limits. Go to G-Solve, second page, integral and root. The cursor appears where the curve crosses the axes, execute and scroll to the next point and execute again. The display gives you both the limits used and the area of the region, which it's shaded for you. Notice the area from the previous integral is still shaded, but it's not included in the answer given.
The mixed integral option covers cases where there is some positive and some negative area in the same question. So explore what happens if you use limits of 0 and 3. The CG50 will also find the area between two graphs. Again, without the need for you to find the points of intersection. This is a really good check for all your work when you're asked to do this calculus in an exam question.
Use F6 or exit to go back to the list of functions. You can edit the existing function by scrolling up and left, and then deleting the terms that you don't need. Execute and enter the second equation. And then draw. If you go to G-Solve, second page, integral and intersection, the cursor appears at a point of intersection. So execute, and then the cursor moves across to the next point of intersection. Execute, and the area between the curves is found. Notice the area here is given us a negative value. This is because Y1 is below Y2 for that whole region and the calculator has used the difference Y1 minus Y2, which is negative throughout that region.
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