Exam (elaborations)
STANDARD INTEGRATION
- Course
- Institution
Understand that integration is the reverse process of differentiation, Evaluate definite and indefinite integrals using basic integration rules.
[Show more]
Seller
Follow
kwazithwala
Content preview
KG THWALA MATE1B1 2020Assignment HW6 due 09/18/2020 at 11:59pm SAST
1. (1 point) 4. (1 point)
Evaluate the indefinite integral. Evaluate the definite integral.
Z e8
dx
(arctan x)2
Z
dx 1 x(1 + ln x)
1 + x2
Answer(s) submitted:
Answer: +C • ln[81]/[2]
Answer(s) submitted: (correct)
• [[arctan(x)]ˆ(3)]/3 Correct Answers:
• 2.19722457733622
(correct)
Correct Answers: 5.
Z (1 point) Find the following indefinite integrals.
x
• (arctan(x))ˆ √ dx = +C
x +4
cos(t)
Z
2. (1 point) dt = +C
(4 sin(t) + 12)2
Evaluate the indefinite integral. Answer(s) submitted:
• [2(x-8)sqrt(x+4)]/3
e2x • -1/[16sin(t)+48]
Z
4x
dx
e +4 (correct)
Correct Answers:
• 2*(x + 4)*sqrt(x + 4)/3 - 2*4*sqrt(x + 4)
Answer = +C • -1/(4*(4*sin(t) + 12))
Answer(s) submitted: Z √
5
• [tanˆ(-1)[(eˆ(2x))/2]]/4 6. (1 point) ex dx = +C
Answer(s) submitted:
(correct)
Correct Answers: • 5eˆ(x/5)
• (1/(2*2))*arctan(eˆ(2 * x)/2) (correct)
Correct Answers:
• 5*eˆ(x/5)
3. (1 point) Find the indicated integrals.
ln(x5 ) 7. (1 point) Note: You can get full credit for this problem by
Z
(a) dx = +C
x just entering the answer to the last question correctly. The initial
Z t
e cos(e )t
questions are meant as hints towards the final answer and also
(b) dt = +C
4 + 4 sin(et ) allow you the opportunity to get partial credit.
Z 5/4 −1 4 Consider the indefinite integral
sin 5x
(c) √ dx =
25 − 16x2 9
Z
0
Answer(s) submitted: dx
9 + ex
• [5lnˆ(2)(x)]/2 The most appropriate substitution to simplify this integral is
• [ln(sin(eˆ(t))+1)]/4 u = f (x) where
• [piˆ(2)]/32
f (x) =
(correct) We then have
Correct Answers: dx = g(u) du
• 5*(ln(x))ˆ2/2 where
• ln(4+4*sin(eˆt))/4 g(u) =
• 0.308425137614586 Hint: you need to back substitute for x in terms of u for this
part.
1
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller kwazithwala. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.55. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75632 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now