Question

To evaluate the definite integral using the Fundamental Theorem of Calculus Part 2, you can use the given antiderivative F(x)=x3−6x2+7x+1. If the definite integral is not provided, you would use the formula:

∫abf(x)dx=F(b)−F(a).

Answer 1

To evaluate a definite integral using the Fundamental Theorem of Calculus Part 2, substitute the limits of integration into the provided antiderivative and subtract to find the integral's value, which represents the total area under the curve of the function from one point to another.

Step-by-step explanation:

The student is seeking to understand how to evaluate a definite integral using the Fundamental Theorem of Calculus Part 2. If given the antiderivative F(x) = x^3 - 6x^2 + 7x + 1, and the limits of integration from a to b, the student can evaluate the definite integral by computing F(b) - F(a). This process involves substituting the upper limit of integration into the antiderivative to get F(b), subtracting the antiderivative evaluated at the lower limit F(a), and then finding the difference between these two values.

Definite integrals represent the total accumulation of quantity, such as the area under a curve between two points on a graph. In the context of the problem, the student likely needs to find the area under the curve of a function f(x) from x1 to x2, as depicted in a diagram which illustrates the sum of infinitesimal strips, forming the integral of f(x) over the interval [x1, x2].