HP 39GS HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 59

Signed area... Another very useful tool provided in the menu is the Signed Area tool. Before we begin to use it, make sure that is switched on, and that the cursor is on F1(X) - the quadratic. The Signed Area tool is similar to the Box Zoom in that it requires you to choose start and end points of the area to be calculated. Definite integrals 3 Suppose we want to find the definite integral: ∫ x2 − 5x − 4 dx −2 Choose and then Signed Area. At the bottom of the screen you will see a prompt, as shown right, asking you to choose a starting point. Press the key, enter the value -2 and press or ENTER. The starting value will then be -2 so press again (or ENTER) to accept it. Another menu will now pop up, asking you to choose what area you wish to calculate. In this case there are only two choices: between F1(X) and the x axis, or between F1(X) and F2(X). If we had defined more functions in the SYMB view then this menu would be longer. In this case we want the area between F1(X) and the x axis, so position the highlight as shown and press ENTER. The graphs will then reappear, with a message requesting that you choose an end point. In the screenshot shown right I have pressed and entered the value 3 to move to that point directly. If you now press ENTER again to accept the end point, the hp 39gs or hp 40gs will calculate the signed area and display the result at the bottom of the screen. Calculator Tip It should be clearly understand that although the label at the bottom of the screen is Area it is a little misleading. What has actually been calculated is the definite integral (right), with 'areas' below the x axis included as negatives. This is why the label on the original menu reads "Signed area" instead of just "Area". 2nd point ∫ F1(X ) dx 1st point 59