9. Consider the indefinite integral sin³ (x) dx. a. Explain why the substitution u = sin(x) will not work to help evaluate the given integral. b. Recall the Fundamental Trigonometric Identity, which states that sin² (x) + cos² (x) = 1. By observing that sin³(x) = sin(x) · sin²(x), use the Fundamental Trigonometric Identity to rewrite the integrand as the product of sin(x) with another function. c. Explain why the substitution u = cos(x) now provides a possible way to evaluate the integral in (b). d. Use your work in (a)-(c) to evaluate the indefinite integral ſ sin³(x) dx. e. Use a similar approach to evaluate cos³(x) dx.

9. Consider the indefinite integral sin³ (x) dx. a. Explain why the substitution u = sin(x) will not work to help evaluate the given integral. b. Recall the Fundamental Trigonometric Identity, which states that sin² (x) + cos² (x) = 1. By observing that sin³(x) = sin(x) · sin²(x), use the Fundamental Trigonometric Identity to rewrite the integrand as the product of sin(x) with another function. c. Explain why the substitution u = cos(x) now provides a possible way to evaluate the integral in (b). d. Use your work in (a)-(c) to evaluate the indefinite integral ſ sin³(x) dx. e. Use a similar approach to evaluate cos³(x) dx.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Hello, thank you for your answer but where is the rest?

A: given figure

Q: Hello, can you explain the first section of the question. Thank yu

A: Function f(x,y) take maximum and minimum value at its critical points

Q: (a) f'(0) (b) f'(1) (c) f'(2) (d) f'(3)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A farmer in Indiana wants to examine the relation between the number of very hot days (days when the…

A: Hey, since there are multiple subparts posted, we will answer first three questions in 2nd page. If…

Q: Number 9 was not answered. I ask for 5 and 9 not 5 and 6. Thank you.

A: We find linear function using table and then find f(0).

Q: t the success due to the news paper publi

A: Among 6 events if 2 resulted in a blockbuster 2 events are successful 4 events are unsuccessful Let…

Q: I do not understand the format of your answer. Please answer in a different format

A: Given: The series is ∑n=1∞ncos nπ2n. To determine: Test for convergence. Test used: Leibnitz's test…

Q: A plane flying from Los Angeles to New York left Los Angeles with 57 passengers on board. The plane…

Q: Hello, I'd like to know how you did the first step. I don't understand how you got there. Thanks

Q: okay can you also do part b now.

Q: last two questions?

A: We will use reduce row Echelon form to find possibilities to convert the given matrix into identity…

Q: can you explain more about the second part that you came up with -2 and 5 . thanks

Q: Thanks for the help! I was also wondering how I would know that the answer would be meaningful?

A: Firstly understand, Y-intercept : it is mean value of y when all predictors (x) equals to 0. X=…

Q: Thank you for your help! I was wondering if the last box with the answer -3 is actually 3?

A: Apologies for the inconvenience. Yes you are right. We are extremely sorry. It was a writing…

Q: A number s is subtracted from seven.When the result is divided by three,the quotient is two. What is…

A: Let a number is s. According to the first condition of the question it becomes 7-s. Now from second…

Q: Hey I cant read what you sent can you please type the answer or write it better

A: We have to find the derivative of v.

Q: John reads that 1 kilometer is equivalent to 0.621 miles. He asks his teacher how many miles there…

A: John's teacher and parents are providing approximate values for the conversion of kilometers to…

Q: I'm really confused and stuck on this question.

A: perimeter = ?

Q: How do I find numbers 2 and 4?

Q: cleared

A: We have to find the digit in thousand place of the product.

Q: Need help solving, thought I knew how to help my son but got myself confused.

A: By using surface area formula, we calculate the required surface area.

Q: Can someone explain how I do numbers 1 and 2 A and B.

A: (1) The weather report get to know about that from the past experiences. For example in the similar…

Q: ssing 2 more questions

A: here we have to use Empirical rule 68% of the values are contained in μ-σ to μ+σ 95% of the values…

Q: This one was confusing thank you for your assistance

A: A snail is travelling along a straight path. the snails velocity can be modelled by v(t)=1.4ln(1+t2)…

Q: Please

Q: I'm sorry , im not fullying understanding how you got the second answer . Can you break it down in…

A: Aa it is given that f(x)=9.44x+84.182*x where f(x) is height of the tree and x is year.

Question

It would be helpful if I could get hand-written explanations as they are easier to read in math than typed. Please and thank you!

9. Consider the indefinite integral ſ sin³(x) dx.
a. Explain why the substitution u = sin(x) will not work to help evaluate the
given integral.
b. Recall the Fundamental Trigonometric Identity, which states that
sin²(x) + cos²(x) = 1. By observing that sin³(x) = sin(x) sin²(x), use the
Fundamental Trigonometric Identity to rewrite the integrand as the
product of sin(x) with another function.
c. Explain why the substitution u = cos(x) now provides a possible way to
evaluate the integral in (b).
d.
Use your work in (a)-(c) to evaluate the indefinite integral ſ sin³(x) dx.
e. Use a similar approach to evaluate ſcos³(x) dx.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

I don't understand how you got 4,-7,1
I have this question on my homework and I don't see a pattern. I have to explain how the trick works. "Think of a number. Add 17. Double the result. Subtract 4. Double the result. Add 20. Divide by 4. Subtract 20. Your answer will be your original number."
First picture is the problem and second question is the question to the problem. Please state answer from the drop down choices.
Still not sure how you came to this answer. Can you elaborate?
I need help explaining. Please explain with words.
I can't tell what the answer is supposed to be. None of the answers are the same as the options and the answer is option -g There is no g. Can you please clear up the answer by writing it legibly.
How do you do a question like this
Could you write out the solution or make it more clear. I can't read the work when it is a jumble of numbers. Thank you.