Question

Someone please help!

Answer 1

Find the integral of sec20tan20do using u substitution

Answer 2

@mathmale

Answer 3

the derivative of what function is sec x tan x ... ?

Answer 4

Reference: http://www.math.com/tables/derivatives/more/trig.htm

Answer 5

Secx

Answer 6

@mathmale sorry had to eat

Answer 7

Good. Hope you're full now.

sec 2x*tan 2x *2 is the derivative of what function?

Answer 8

Be sure to review the Chain Rule if need be.

Answer 9

I have no idea :/

Answer 10

Tanx? I don't know

Answer 11

@zepdrix confused here

Answer 12

Sec^2

Answer 13

but what's your argument?

sec x can't stand alone. Must have an argument.

Answer 14

The derivative of what function is sec 2x tan 2x *2?

Answer 15

Ugh

Answer 16

2secx I really don't know :(

Answer 17

the derivative with respect to x of sec 2x) is sec 2x tan 2x * 2.

But you were asked to find the integral of only sec 2x tan 2x (no 2!).

What function, when differentiated with respect to x, produces the derivative sec 2x tan 2x * 2?

Answer 18

Hold that for a moment (it's correct, but I wanted to ask you to try something else).

Differentiate sec x tan x.

Next, differentiate sec 2x tan 2x.

Are the results the same or different?

You must follow the Chain Rule in the 2nd case.

Answer 19

and the reason for that is that 2x is itself a separate function.

Answer 20

Just give me a second

Answer 21

They aren't the same

Answer 22

Right, they're not.

Look: sec x is a function. But so is 2x.

Thus, if you want to find the derivative wrt x of (sec 2x)^2, you get sec 2x tan 2x times the derivative of 2x (which happens to be 2).

OK with this so far?

Answer 23

Yes

Answer 24

In taking the derivative of 2x, you have successfully applied the Chain Rule.

OK: you wanna do substitution?

Fine. Let u=2x.

Find du/dx.

du/dx=?

Answer 25

Du/Dx=2

Answer 26

Right. You want to integrate sec 2x tan 2x dx.

Since u=2x, and du/dx=2, solve the 2nd equztion for dx now, please. dx=?

Answer 27

1/2du=dx

Answer 28

Right. So, instead of integrating sec 2x tan 2x dx, you're gonna integrate
dy= sec u tan u (du/2).

Answer 29

Gotta get rid of that /2. So, Move that (1/2) to in front of sec u tan u du.

Answer 30

Okay and that makes sense

Answer 31

so now you are integrating (1/2)[sec u tan u du].
What's the integral? Don't forget that (1/2).

Answer 32

Remember you have already successfully integrated sec x tan x dx. SAME THING.

Answer 33

1/2secu

Answer 34

Plus C. ;)

Answer 35

Oh yeah!

Answer 36

And put parentheses around that doggone 1/2, please.

Answer 37

Okay!

Answer 38

So your final answer is ... ? Be careful; you did not start with the variable u; you began with 2x.

So, your final answer is...?

Answer 39

(1/2)sec(2x)

Answer 40

Plus what?

Answer 41

C!

Answer 42

Kool as all get out.

Answer 43

Forgive my pestering you, but we want you to get a very high grade in calculus, don't we?

Answer 44

Yes

Answer 45

go for it! Take care, over and out, bye.

Answer 46

Thank you! :)

Answer 47

:)