Question

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = x2 − 7x + 5

Answer 1

Answer:

F(x) = $\frac{x^3}{3} - \frac{7x^2}{2} + 5x + c$

Step-by-step explanation:

The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;

F(x) = $\int\limits{f(x)} \, dx$

From the question, f(x) = x² - 7x + 5

Therefore,

F(x) = $\int\limits {(x^2 - 7x + 5)} \, dx$

F(x) = $\frac{x^3}{3} - \frac{7x^2}{2} + 5x + c$

Where c is the constant of the integration (antiderivative).

PS: The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.