Barrons AP Calculus

. (C). (B) Rewrite as and use formula (8). (E) Use formula (4) with u = ex − 1; du = ...

(C) Use formula (6) with . (B) Use formula (15) with . (C) Use the Parts Formula. ...

The integral equals . (B) Use parts, letting u = ln η and dv = dx. Then and v ...

(E) The integral equals ; it is equivalent to , where u = 1 − ln t. (A) Replace ...

(E) Use integration by parts, letting u = arctan x and dv = dx. Then . The Parts Formu ...

76. 77. 78. 79. 80. (D) Note the initial conditions: when t = 0, v = 0 and s = 0. Integrate twice: v = ...

(C) The integral is equal to . (B) Rewrite as . This equals . (E) Rewrite as . (B) This ...

(A) (C). (D) You get . (B). (B) Evaluate , which equals . (E). (C) If . When ; ...

(A). (C) Use the Parts Formula with u = x and dv = ex dx. Then du = dx ...

(B) If , then u^2 = x + 1, and 2u du = dx. When you substitute for the ...

is the sum of the areas of two triangles: . (C) Because is a semicircle of radius 8, it ...

(E) The average value is . The integral represents the area of a trapezoid: . T ...

(D) This is theorem (2). Prove by counterexamples that (A), (B), (C), and (D) ...

54. 1. 2. (B) 7 Applications of Integration to Geometry AREA We give below, for each of Questions 1–17, a ...

(A) (D) ...

(D) (C) ...

(E) (A) ...

(A) (D) ...

(D) (C) ...

(D) (A) ...