Definite Integrals Questions and Answers

Let A x represent the area bounded by the graph the horizontal axis and the vertical lines at t 0 and x for the graph below Evaluate A x for x 1 2 3 and 4 5 3 M 2 1 A 1 A 2 1 A 3 A 4 2 3 50

y f x R S 10 1 Let f be the function given by f x x 3cos x Let R be the shaded region in the second 2 quadrant bounded by the graph of f and let S be the shaded region bounded by the graph of and line l the line tangent to the graph of at x 0 as shown above a Find the area of R

DUE MONDAY APRIL 15th YOU 2004 AP CALCULUS AB FREE RESPONSE QUESTIONS y g x 2 Let f and g be the functions given by f x 2x 1 x and g x 3 x 1 x for 0 x 1 The graphs of and g are shown in the figure above a Find the area of the shaded region enclosed by the graphs of f and g y f x g x 0 1 Let f and g be the functions given by f x 1 sin 2x and g x e 2 Let R be the shaded region in the

10 Given to the right is the graph of f t Additionally let the function g x be defined to be ff t dt a Where does the graph of g have a relative max b Where is the graph of g concave down

5 3 For questions 6 8 use the Fundamental Theorem of Calculus to find the derivative of the functions 6 g s t t2 8 dt 7 F x x 3 t dt 8 g x 3 2t 5 dt

3 2 0 1 2 1 4 1 Graph of f 5 2 5 The graph of the function shown above consists of a semicircle and three line segments Let g be the function given by g x t dt a Find g 0 and g 0 b Find all values of x in the open Interval 5 4 at which g attains a relative maximum Justify your answer c Find the absolute minimum value of g on the closed interval 5 4 Justify your answer d Find all values of x in the open Interval 5 4 at which the graph of g has a point of Inflection

For the following find F x F x So COS t2 dt F x 2t 5 dt night La 3x F x Int dt aloupe D S F x t dt 03 x Sandwolfof all to d 1 4 A

b 1 1 y sin e cos 0 tan e csc e sec 0 cot e

Given f x dr 4 f x dz 6 and 6 and 9 2 de 19 dz dx 3 find the following L1 2 dz 2 135 15 3f x g 2 dr 12g 2 dr 0

What are the domain and range of the function f x 2 6 Domain 0 O Range 6 Domain 6 O Range 0 Domain 6 O Range 00 0 Domain 0 O Range 6

7 Simplify each trig expression into one number or an expression with a single trig function 1 CSC x a b sin x cos x tan x C cot a csc x d 1 sin x 1 tan x

2 2 2 4 2 4 Graph of f C 10 5 6 7 2 3 The graph of a function f is shown above What is the value of S A 6 B 8 f x dx D 14 E 18

1 Alvaro is studying the extinction of the bear population of Siberia over time The following function gives the number of bears t years since Alvaro started tracking it B t 2190e 0 3t a What is B 3 b Interpret B 3 in the context of tis problem

Solve the equation Write the solution set with the exact values given in terms common or natural logarithms e2y7ey 12 0

4 g x 5 at x 4 X