Question

Find the antiderivative for the function f(x) = (x – 11)(x +13).

A. -1/2 x³+x² – 123x+C
B. – 1/2 x³+13x² – 123x+C
C. 1/3 x³+x² – 143x +C
D. 1/3x³+13x² – 143x + C

Answer 1

The antiderivative of the function f(x) = (x – 11)(x +13) is F(x) = (1/3)x^3 + x^2 - 143x + C after expanding and integrating term by term.

Step-by-step explanation:

To find the antiderivative of the function f(x) = (x – 11)(x +13), you need to first expand the function and then integrate term by term. Expanding the function gives us:

f(x) = x^2 + 13x - 11x - 143

Which simplifies to:

f(x) = x^2 + 2x - 143

The antiderivative of this function is:

1. For x^2, the antiderivative is (1/3)x^3
2. For 2x, the antiderivative is x^2
3. For -143, the antiderivative is -143x

When you combine these and add the constant of integration (C), the antiderivative of f(x) is:

F(x) = (1/3)x^3 + x^2 - 143x + C