Question

can anyone help me answer these questions? (attached in picture below)

Answer 1

Sure, Douglie. But may I ask you to identify which ones you've already been able to do, and to share with me an image of your work, first?

Answer 2

I'd like to know where you're coming from (that is, what you already know and understand).

Answer 3

I'm not sure how to do any of them haha sorry I found this topic extremely confusing.
for number 2, I got up to (16 cos^2(x)+sec^2(x)+8) dx by distributing the power but that's pretty much it..sorry

Answer 4

Have you used substitution to integrate simpler (algebraic) expressions? If so, what's the purpose of substitution, as you see it?

Answer 5

It's to make the expression easier to integrate

Answer 6

Right. Same when we integrate trig functions. Which of the problems would you like to begin with?

Answer 7

#1 I don't get how to do it with the u as sin3x

Answer 8

I'll need to take a quick look at your illusstration. be right with you. have you any idea of how to start?

Answer 9

I think du= 3cos(3x) ?

Answer 10

that'd be perfect if you were to add "dx" to the end. du-3cos(3x)dx.

Answer 11

Now, DD, compare that du to what you actually have in the integral given. Does the integral have 3cos(3x)dx?

Answer 12

oh so it becomes integral u du?

Answer 13

Yes, just about. But please answer my question specifically.

Answer 14

the du is cos3xdx do you can substitute that into the original integral

Answer 15

Almost. You correctly found that du=3cos(3x)dx.
But you don't have

Answer 16

that 3.

Answer 17

In summary, you calculated (correctly) that du=3cos(3x)dx,
but the given integral has only cos(3x)dx. My question: What do we need to do

Answer 18

next?

Answer 19

You've probably dealt with this kind of situation before. If du=3cos(3x)dx, you could divide both sides of this equation by 3. Then the right side would be cos(3x)dx, right? What would the left side be?

Answer 20

ohhh so I put in 1/3 u?

Answer 21

Actually, that would be \[\frac{ du }{ 3}\]

Answer 22

Take a deep breath and ask yourself how to put the simpler integral together.
Replace sin(3x) with what?
Replace cos(3x)dx with what?
What does the re-written integral now look like?

Answer 23

so we replace sin3x with u, cos3xdx with du/3 and then the integral is u du/3

Answer 24

Perfect. Go ahead and integrate now. When you're finished, replace that u with sin(3x).

Answer 25

that's where I think I go wrong haha is it u^2/2 * 3u^1/3 really don't know that part

Answer 26

Just a moment, please...

Answer 27

\[\int\limits_{-}^{-}u \frac{ du }{ 3}=\frac{ 1 }{ 3 }\int\limits_{-}^{-}udu\]

Answer 28

First, ignore the 1/3. Integrate udu. Result? Now mult. the result by 1/3 and add "+c) to the end.

Answer 29

Do youhave some way of showing me what you have actually written? For example, do you ever use the Draw feature (below)?

Answer 30

DD?

Answer 31

sorry my internet froze!!

Answer 32

okay I understand number one! thanks so much!!! if there any wy you can help me with the others?

Answer 33

Sure. I'd like to get off the computer soon, so would you please pick one more problem from that list. I'd also suggest that you do as much work as y ou can on the remaining problems and be prepared to share with me images of what you've done.

Answer 34

okay can we for in number 3?

Answer 35

I'm not sure what using partial fractions even means haha

Answer 36

Let me take a quick look at #3.