Barrons AP Calculus - David Bock

SOLUTIONS: See Figure N6–21b. (a) g(b) is the slope of G(x) at b, the slope of line ST. (b) is equal to the area under G(x) from ...

(f) F(6) = (g) In Figure N6–22b we evaluate the areas in the original graph. FIGURE N6–22b Measured from the lower limit of inte ...

topic. Practice Exercises Part A. Directions: Answer these questions without using your calculator. 1. (A) (B) 0 (C) (D) −2 (E) ...

5. (A) ln 3 (B) (C) (D) ln (E) (A) 1 (B) (C) (D) −1 (E) 2 (A) (B) 6 (C) (D) 0 (E) 4 (A) (B) (C) (D) (E) (A) (B) ...

(C) (D) (E) 10. (A) (B) 1 − e (C) (D) (E) (A) e − 1 (B) (C) 2(e − 1) (D) (E) (A) 2 (B) (C) −1 (D) (E) −2 (A) −ln 2 ( ...

If we let x = 2 sin θ, then is equivalent to (A) (B) (C) (D) (E) none of these (A) (B) (C) 1 (D) (E) 0 (A) (B) (C) 0 (D) 1 ( ...

(B) (C) (D) (E) 19. (A) (B) (C) (D) ln 3 (E) (A) (B) (C) (D) −1 (E) (A) (B) 1 (C) (D) (E) −1 (A) e (B) 2 + e (C) (D) ...

(E) e − 1 (A) ln 2 (B) e (C) 1 + e (D) −ln 2 (E) If we let x = tan θ, then is equivalent to (A) (B) (C) (D) (E) If the su ...

(A) −1/2 (B) −3/8 (C) 3 (D) 4 (E) none of these Using M(3), we find that the approximate area of the shaded region below is (A) ...

(A) (B) (C) (D) (E) Let We estimate A using the L, R, and T approximations with n = 100 subintervals. Which is true? (A) L < ...

(D) (E) The average value of on its domain is (A) 2 (B) 4 (C) 2π (D) 4π (E) none of these The average value of cos x over the i ...

(A) 2 (B) 4 (C) 5 (D) 7 (E) 8 The integral gives the area of (A) a circle of radius 4 (B) a semicircle of radius 4 (C) a quadr ...

In which of these intervals is there a value c for which f (c) is the average value of f over the interval [0,6]? I. [0,2] II. ...

(A) (B) f ′(c)(b − a) (C) f (c)(b − a) (D) (E) f (c)[f (b) − f (a)] If f (x) is continuous on the closed interval [a,b] and k i ...

(D) (E) If x = 4 cos θ and y = 3 sin θ, then is equivalent to (A) (B) (C) (D) (E) A curve is defined by the parametric equation ...

I. II. III. (A) II only (B) III only (C) I and II only (D) I and III only (E) II and III only Find the value of x at which the ...

CHAPTER 7 Applications of Integration to Geometry Concepts and Skills In this chapter, we will review using definite integrals t ...

If f (x) changes sign on the interval (Figure N7–2), we find the values of x for which f (x) = 0 and note where the function is ...

See Questions 4, 6, 7, and 9 in the Practice Exercises. FIGURE N7–4 A2. Using Symmetry. Frequently we seek the area of a region ...

Evaluating Using a Graphing Calculator The calculator is especially useful in evaluating definite integrals when the x-intercept ...