math

I JUST NEED 1C

MATHEMATICAL METHODS FOR ENGINEERS 2 and CALCULUS 2

Assignment 3 – due Thurs 24th Oct, 4pm

Please use a cover sheet and submit (together with the assignment question(s) from tutorial 9)
via the MME2 (or Calculus 2, if appropriate) assignment box in the OC building. Make sure
you include your tutor’s name and tutorial day/time on your cover sheet.

Late submission incurs a penalty of 10% per day, up to 40%. Work more than 4 days late will
not be accepted.

1. (a) Evaluate
!

3×5 sin(x3) dx

(b) Evaluate
! !/6

0

sin(4x) cos(2x) dx

(c) Consider the circle given by x2 + y2 = a2. Use a trig

(or hyperbolic trig) substitution to find the area within the

circle such that 1
2
a ! x !

”
3

2
a.

Tutorial 8. Week 9

1. Evaluate the following integrals.

(a)
! !2/

”
3

!2

dx

x
”
x2 # 1

(b)
!

3

0

dx

9 + x2

(c)
!

”
12

0

dx
”
16 # x2

(d)
!

3

1

dx

2
”
x(1 + x)

(e)
!

2

!3

dx
”
16 # 6x # x2

Additional questions: Edwards and Penney, 7/e, Section 6.8, Questions 37, 40, 45, 53.

MATHEMATICAL METHODS FOR ENGINEERS 2 and CALCULUS 2

Assignment 3 – due Thurs 24th Oct, 4pm

Please use a cover sheet and submit (together with the assignment question(s) from tutorial 8)
via the MME2 (or Calculus 2, if appropriate) assignment box in the OC building. Make sure
you include your tutor’s name and tutorial day/time on your cover sheet.

Late submission incurs a penalty of 10% per day, up to 40%. Work more than 4 days late will
not be accepted.

2. Evaluate
!

6×2 + 12x + 14

x3 + 3×2 + 7x + 5
dx

3. This question will be similar to Q3 from Tutorial 9. It will be given to you in your
tutorial in Week 11. It should be completed and submitted to your tutor at the end of
the allocated time. The relevant section of the formula sheet on the course website will
be provided – no other notes are allowed, no calculators allowed. Note that each
tute class will have a di!erent question.

Tutorial 9. Week 10

1. Find the integrals.

(a)
!

dx

x2 ! 3x

(b)
!

x4 dx

x2 + 4

(c)
!

x + 10

2×2 + 5x ! 3
dx

Additional questions: Edwards and Penney, 7/e, Section 7.5, Questions 18, 29, 51.

2. From previous examination

Use partial fractions to find

!
20x ! 30

x(x ! 2)(x2 ! 2x + 5)
dx.

3. Do the improper integrals below converge? Evaluate those that do converge.

(a)
!

!

1

1

x + 1
dx

(b)
!

!

5

1

(x ! 1)3/2
dx

(c)
!

!

0

xe”3x dx

(d)
!

!

0

xe”x
2

dx

(e)
!

!

0

1

x2 + 1
dx

(f)
!

!

0

1

x2 + x
dx