AP Calculus AB Unit 8.4: Area Between Curves

Practice AP Calculus Unit 8.4 questions on setting up and evaluating definite integrals for area between two curves over a stated interval.

Covered syllabus points

[Maximum number: 2]

The shaded region R is bounded by the graphs of the functions f and g, where $f(x)=x^{2}-2 x$

and $g(x)=x+\sin (\pi x)$ , as shown in the figure.

(Note: Your calculator should be in radian mode.)

Find the area of R. Show the setup for your calculations.

A	Find the area of R. Show the setup for your calculations.
		$\int_{0}^{3}(g(x)-f(x)) d x$	Form of integrand Point 1 (P1)
		= 5.136620	Answer Point 2 (P2)
		Scoring Notes for Part A
		- P1 is earned for a response that presents an integrand of g(x)-f(x),\|g(x)-f(x)\|, f(x)-g(x), or \|f(x)-g(x)\| in a definite integral, with or without the differential d x. - P2 is earned for the correct answer, with or without supporting work. A reported answer should be accurate to three places after the decimal point, rounded or truncated. An inappropriately rounded answer does not earn the point. - Incorrect communication between the integral and the correct answer is treated as scratch work and is not considered in scoring. Note: This response earns P1 for the integral. It also earns P2 for the correct answer. Note: This response earns P1 for the integral. It also earns P2 for the correct answer. (In this instance, incorrect linkage is not considered in scoring.)

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