MATH2080 Assignment #1

MATH*2080W15 – Assignment
#1

INSTRUCTIONS

1.
Print this blank assignment
right now. You’ll be completing the following 4 pages, writing a summary of
your solutions here, and submitting this completed assignment. No extra paper
please – I won’t accept it.

2. Note that there is space
provided for summary work related to each question. DO NOT cram every step into
each answer space – but instead – transfer key steps from your rough work. For
example, if you prepare a set of equations for solution using Partial
Fractions, then show me how you get the equations. Then simply state that after
solution the answers are etc. Or, when you perform integration, show me the
start, the substitution, the completed set-up, and then say something like,
after simpli cation. Then show me the nal step just before you integrate.

3. MAKE A BOX AROUND YOUR
FINAL ANSWER TO MAKE IT EASIER TO LOCATE AND GRADE (thank you)

4. You are encouraged to work
together. PLEASE – PLEASE – write-up your own solutions and submit your own
individual write-up.

5. This assignment is worth
13% of your nal grade, graded in 1/2 %
units.

Assignment #1 MATH*2080W15

Surname:

Initials:

(PRINT)

Student #:

Grade:

1.
(1

mark)
Solve

R

p

36x 36

dx using the chain rule
in reverse (CHIR). GIFT!

2

36(x 1)2

9

2. (1 mark) Solve

p

36x 36

9

dx using the substitution u = x

1
followed by a trigonometric substitution.

36(x

1)2

ANOTHER

GIFT!

R

c S.J. Gismondi
(Instructor), 2015. All rights reserved.

1

marks) SolveR

x

3. (1

dx
anyway you can. FUN!

2

1+cos(x2)

4.
(2 marks) Solve

p

36x 35

dx. DO THE HINT EXACTLY!

R

36×2 72x+27

HINT:
Adjust the expression by a multiplicative constant and then add and subtract
whatever may be needed so that you can break the integral into two pieces. Why?
Use CHIR (chain rule in reverse) on one of the pieces. Then complete the square
under the root and use an appropriate trigonometric substitution to solve the
second integral. Welcome to MATH2080! Don’t ya just love it?

c S.J. Gismondi
(Instructor), 2015. All rights reserved.

R
5.
(112
marks) Solve x3ex2
dx using Integration by Parts. A THINKER!

R
6.
(212
marks) Solve sec5(x)dx
using Integration by Parts. RECALL sec3(x)
from class notes!

c S.J. Gismondi
(Instructor), 2015. All rights reserved.

7. (2

1

marks) Solve

x44 x332x2 2x+4

dx using
partial fractions. VERY TRICKY & A LONG SET-UP!

2

x 5x +10x+24

(Don’t
show me

all the
set-up … just tell me in a sentence and get on with the task.)

R

1

marks)
SolveR

x2+2x+2

8. (1

dx using
partial fractions. STRAIGHT-UP APPLICATION!

2

(x2+1)(x 1)2

c S.J. Gismondi
(Instructor), 2015. All rights reserved.