In calculus, the indefinite integral is the most general form of an anti-derivative for a function. This means, given a function F(x) and its derivative f(x), F(x) is the anti-derivative of f(x). The indefinite integral of f(x) is therefore F(x) + c, where c is any constant. Indefinite integrals represent families of functions where the only difference between functions is c. The derivative of F(x) is always equal to f(x), no matter the value of c, as the derivative of any constant is 0. Solving an indefinite integral on a TI-84 Plus makes it simple to check your work graphically.
Press the Y= button and move the cursor to the first open Y= area. If you have no other equations present, this area will be Y1.
Enter the "find integral" command, fnInt. To use this command, paste it into the Y= field by pressing the MATH button, then press 9 to choose the fnInt( command. The syntax within the parentheses for this command are fnInt(function, variable used, lower bound, upper bound).
Enter the appropriate values into the fnInt command. For example, in order to find the indefinite integral of x^3, substitute T for x and enter fnInt(T^3, T, 0, X). In this case, the lower bound is 0 and the upper bound varies with X.
Notice the graph looks a lot like x^4, which is a parabola like x^2 but more steep. Using anti-differentiation rules, the anti-derivative is actually (x^(3 + 1) / (3 + 1)) = (x^4 / 4). If you graph (x^4 / 4) alongside the indefinite integral of x^3, you will see they are the same graph.
Things you need
- TI-84 Plus graphing calculator