Calculus II Practice Exam PDF

Math 022 Calculus II Exam 1 - Practice Exam This is a 60-minute exam. Answer all of the following questions and note that the exam is double-sided. No books, notes, calculators, phones, or any other devices are allowed during the exam, for an...

Math 022 Calculus II Exam 1 - Practice Exam This is a 60-minute exam. Answer all of the following questions and note that the exam is double-sided. No books, notes, calculators, phones, or any other devices are allowed during the exam, for any reason. Any students who violate this policy will receive a zero on the exam. Please be sure to show your work and provide reasoning for all of your answers (unsupported answers may not receive credit). As always, you are expected to adhere to the Lehigh University Student Code of Conduct. Name: Section number: Question Score Total 1 2 3 4 5 6 7 Notation Total 1. Let R be the region under y = sin(x), between x = 0 and x = π. This region is shown in the picture below: y y=0 y = sin x (a) Compute the volume V of the solid obtained by revolving the region R about the x-axis. (b) Compute the volume V of the solid obtained by revolving the region R about the y-axis.  √ 2. (a) Compute the average value of the function f (x) = x on the interval [0, 9]. (b) For the function f (x) given in part (a), find all values of c in the interval [0, 9] at which f (c) = fave. 3. Evaluate the following integrals. Z 1 (a) x2 e−x dx. 0 Z (b) ex sin(x) dx. 4. Compute the following trigonometric integrals. Z (a) sin2 (x) cos5 (x)dx. Z (b) tan3 (x) sec3 (x)dx  Z 1 5. Evaluate the following integral: √ dx x2 x2 − 4  7x3 − 3x2 + 12x − 4 Z 6. Evaluate: dx. x4 + 4x2 Z 7. Evaluate: arctan(x) dx.