AP Calculus AB 8.4: Area Between Curves

Practice AP Calculus questions on setting up and evaluating definite integrals for the area between two curves over an interval.

[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.)

All question bank results loaded

CHA-5.A—Calculate areas in the plane using the definite integral question 1