University of Ottawa -

pdf

School

University of Ottawa *

*We aren’t endorsed by this school

Course

1330A

Subject

Mathematics

Date

Apr 3, 2024

Type

pdf

Pages

6

Uploaded by HighnessRoseGuineaPig14

Report
2023-11-30, 11 : 54 PM University of Ottawa - Page 1 of 6 file:///Users/bharat/Desktop/University%20of%20Ottawa%20-%20inegral%20practice.html Online Homework System Assignment Worksheet 11/30/23 - 6:52:24 PM EST Name: ____________________________ Class: MAT1330A : Calculus for the Life Sciences I, Fall 2023 Class #: ____________________________ Section #: ____________________________ Instructor: Monica Nevins Assignment: Homework 9 Fall 2023 Question 1: (1 point) Using the method of substitution, determine which of the following represents . (a) (b) (c) (d) Question 2: (1 point) Setting , which of the following is equivalent to ? (a) (b) (c) (d) dx 2 x 1 + x 4 + C x 2 x + 1 5 x 5 arctan( ) + C x 2 + C x 2 1 + x 4 ln(1 + ) + C x 2 x 4 u = x 2 ln( ) dx x 3 x 4 ln( ) du 1 2 u u 2 ln( ) du 1 3 u u 3 ln( ) du 1 2 u 2 u 2 ln( ) du 1 3 u 2 u 2 1
2023-11-30, 11 : 54 PM University of Ottawa - Page 2 of 6 file:///Users/bharat/Desktop/University%20of%20Ottawa%20-%20inegral%20practice.html (e) (f) Question 3: (1 point) Setting , which of the following is equivalent to ? (a) (b) (c) (d) (e) (f) Question 4: (1 point) With the substitution , we get where the resulting integrand is __________ . FORMATTING: We write trigonometric powers in long form in Mobius. For example is written . ln( ) du 1 2 u u 3 ln( ) du 1 3 u u 2 u = x 2 dx tan( ) x 8 x 3 du 1 3 tan( ) u 4 u 2 du 1 2 tan( ) u 5 u 2 du 1 2 tan( ) u 4 u du 1 3 tan( ) u 4 u du 1 3 tan( ) u 5 u 2 du 1 2 tan( ) u 4 u 2 u = sin(5 x ) d x = f ( u )d u cos(5 x ) (5 x ) sin 3 f ( u ) = ( x ) cos 2 (cos( x )) 2
2023-11-30, 11 : 54 PM University of Ottawa - Page 3 of 6 file:///Users/bharat/Desktop/University%20of%20Ottawa%20-%20inegral%20practice.html Question 5: (1 point) Compute the indefinite integral __________ where is the constant of integration. Do not include the constant of integration in your answer as we have already done so. Question 6: (1 point) Compute the indefinite integral __________ where is the constant of integration. Do not include the constant of integration in your answer as we have already done so. Question 7: (1 point) Compute the indefinite integral __________ where is the constant of integration. Do not include the constant of integration in your answer as we have already done so. dx = (3 x + 3) 3 + C C dx = e x + 1 e x + C C dx = e x (2 + 4 ) e x 2 + C C
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
2023-11-30, 11 : 54 PM University of Ottawa - Page 4 of 6 file:///Users/bharat/Desktop/University%20of%20Ottawa%20-%20inegral%20practice.html Question 8: (1 point) Compute the indefinite integral __________ where is the constant of integration. Do not include the constant of integration in your answer as we have already done so. Question 9: (1 point) Compute the indefinite integral = __________ + C. Do not include the constant of integration; we have already included it for you. Question 10: (1 point) Consider the indefinite integral We wish to use integration by parts. To this end, what are the best choices for the parts and so that ? Answer: __________ , __________ . Now compute the integral using integration by parts as many times as necessary. __________ , where represents the integration constant. FORMATTING: Do not include the integration constant in your answer, as we have included it for you. dx = e x ( ) cos 2 e x + C C dx e 5 x +2 - - --- 5 x + 2 - - --- sin(4 x ) dx . x 2 f g sin(4 x ) dx = f ( x ) ( x ) dx x 2 g f ( x ) = ( x ) = g sin(4 x ) dx = x 2 + C C
2023-11-30, 11 : 54 PM University of Ottawa - Page 5 of 6 file:///Users/bharat/Desktop/University%20of%20Ottawa%20-%20inegral%20practice.html Question 11: (1 point) The goal of this exercise is to use integration by parts to evaluate the following indefinite integral: Choose the best parts and so that we can rewrite the integral as follows: What are the parts and ? __________ __________ Now, find and . __________ __________ Finally, use integration by parts to evaluate the integral: __________ . FORMATTING: Your answer should not involve any absolute values; the integrand is only defined for . Do not include the integration constant in your answer, as we have already written " " for you. Question 12: (1 point) Compute the indefinite integral __________ , where represents the integration constant. FORMATTING: Your answer should not involve any absolute values, since the integrand is only defined for . Do not include the integration constant in your answer, as we have included it for you. Question 13: (1 point) d x . ln( x ) x 3 f g d x = f ( x ) ( x )d x . ln( x ) x 3 g f g f ( x ) = ( x ) = g f g ( x ) = f g ( x ) = d x = ln( x ) x 3 + C x > 0 + C ln( x ) dx = x 3 + C C x > 0
2023-11-30, 11 : 54 PM University of Ottawa - Page 6 of 6 file:///Users/bharat/Desktop/University%20of%20Ottawa%20-%20inegral%20practice.html Compute the indefinite integral __________ , where represents the integration constant. Do not include the integration constant in your answer , as we have included it for you. cos(4 x ) dx = x 2 + C C
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help