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Chapter 5: Integrals and the Fundamental Theorem
Goals
- Evaluate a definite integral using the Fundamental Theorem of calculus and using technology.
- Interpret the definite integral
 where F'(x) = f(x) as the area between y = f(x) and y = 0 from x = a to x = b.
- Interpret the definite integral where F'(x) = f(x) as the net change of y = F(x) from x = a to x = b.
- Calculate the total distance traveled by a moving body between t = a and t = b where y = v(t) is the velocity of the moving body.
- Find the area between two curves given boundaries.
- Graph a family of solutions to a differential equation.
- Find the antiderivative or the indefinite integral of a given
function using the toolkit of derivatives, substitution of variables, partial fractions, or table of integrals.
- Find the general or particular solution to a differential equation using separation of variables.
- Interpret
 in two ways: as f'(x) where y = f(x) and as the ratio of two differentials, dy and dx.
- Approximate the value of a definite integral by the Riemann sum, summing areas of rectangles, or summing areas of trapezoids.
- Find a model of quadratic, exponential, or logistic data by solving a differential equation developed from the difference quotients of the data.
- Find the equation of the linear least squares line through linear data.
- Calculate and plot the residuals of a model to data.
- Create a list of difference quotients from a given set of data.
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