Question

definite integral question

Answer 1

\[\int\limits_{1}^{5} 1/(\sqrt{4x + 5}) dx\]

Answer 2

i did

\[\int\limits_{1}^{5} (4x + 5)^ {-1/2} dx\]

u = 4x + 5
du = 4dx
1/4du = dx

\[1/4 \int\limits\limits_{1}^{5} (u)^ {-1/2} dx\]

Answer 3

change your limits...

Answer 4

1/4 2u^1/2 | 5 and 1

Answer 5

what you did is correct, but you might as well change the limits of integration at the same time so you don't have to substitute back

Answer 6

if you are going to use 1 and 5, you have to change \(u\) back to \(4x+5\)

Answer 7

1/4 [2((4 * 5) + 5) - 2((4 * 1) +5]

1/4 (2 * 25) - (2 * 9)

1/4(50 -18)

1/4 (32) = 8

Answer 8

if you want you can start with \(u=4x+5,u(1)=9,u(5)=49\) and then use
\[\frac{1}{4}\int_9^{49}u^{-\frac{1}{2}}du\]

Answer 9

what dpalnc said

Answer 10

cough cough 4(5)+1 equals....

Answer 11

oops 4(5)+5 whatever

Answer 12

25 :P

Answer 13

yeah, 49, 25, whatever

Answer 14

49,21, or 25

Answer 15

some perfect square or another

Answer 16

safest one to go with is 25 though

Answer 17

72!

Answer 18

hike

Answer 19

hello myininaya
doesn't anyone go out boozing on saturday night?

Answer 20

i'm sleepy. just got back from California.

Answer 21

I guess I'm confused when I switch the limits up or not, I guess i used u = 4x +5 so I had to change the limits to u.

If I used x I would have to say u = 4x + 5 and x = u/4 -5?

Answer 22

you are a vacationing somebody aren't you?

Answer 23

right make sure you use the substitution on the limits too :)

Answer 24

no if you do not change the limits you replace \(u\) by \(4x+5\) at the end , then evaluate

Answer 25

so if I was using x = u/4 -5 the limits would still be 1-5 right?

Answer 26

oh.. hmm..

Answer 27

oh no hold on

Answer 28

x = (4u +5) = (4(4x + 5) +5) :P

Answer 29

EITHER change the limits at the beginning, or change back to \(4x+5\) and the end before you evaluate
convince yourself that it doesn't matter and that you get the same answer in any case

Answer 30

you are making it much harder than it is
want to start at the beginning?

Answer 31

Isn't that what I did though changing it back to 4x+5?

Answer 32

Ok lets do it without changing the limits .... and then after integrating put back in terms of x and then apply the limits

Answer 33

yeah your answer is right

Answer 34

1/4 [2((4 * 5) + 5) - 2((4 * 1) +5]

1/4 (2 * 25) - (2 * 9)

1/4(50 -18)

1/4 (32) = 8

Answer 35

Ok lets do this! :)

Answer 36

oh wait, it is not right
anti derivative of
\[\frac{1}{\sqrt{u}}\]is
\[2\sqrt{u}\]

Answer 37

you need the square root sign there and you do not have it

Answer 38

\[1/4 * 2(u)^{1/2}\]

Answer 39

\[\frac{1}{4}\int\frac{du}{\sqrt{u}}=\frac{1}{2}\sqrt{u}\]

Answer 40

Ok so that was another thing I was curious about if I just do 2 * 1/4 ok.

Answer 41

yes they are constants

Answer 42

ok so it should be 1/2[ (4 * 5 + 5) - (4 + 1 + 5)] = 25 - 9 = 14 *1/2 = 7?

Answer 43

\[\int\limits_{1}^{5}\frac{1}{\sqrt{4x+5} } dx\]

You did good to let u=4x+5
du=4 dx
du/4=dx

\[\int\limits_{C}^{}\frac{1}{\sqrt{u}} \frac{du}{4} \]

\[\frac{1}{4}\int\limits_{C}^{} u^\frac{-1}{2} du\]
So you integrate here
Then use u=4x+5
then you can do
\[F(x)|_1^5=F(5)-F(1)\]
Where F is the antiderivative of \[\frac{1}{\sqrt{4x+5}}\]

Answer 44

Did I make that understandable?

Answer 45

Or should I put some more steps in?

Answer 46

I guess more steps, we are trying to now find "C" The Function is 4x+5 so it would be 25 and 9 but would that be the integral? What would we be finding? would it be x then @ x = u/4 -5?

Answer 47

and would 7 be the correct answer?

Answer 48

Yes you have the limits right

Answer 49

\[\frac{1}{4} \cdot \frac{u^\frac{1}{2}}{\frac{1}{2}}|_9^{25}\]
\[\frac{1}{4} \cdot 2 u^\frac{1}{2}|_9^{25}=\frac{1}{2}u^\frac{1}{2}|_{9}^{25}\]
\[\frac{1}{2}(25^\frac{1}{2}-9^\frac{1}{2})\]
hmmm.... I'm getting something different ....
Did I make a mistake?

Answer 50

You did do the antiderivative above I see...

Answer 51

And it seems the same as mine...

Answer 52

oh woops I for ot the ^1/2 :P

Answer 53

if you forgot that it would be 8 right ? lol

Answer 54

so it should be 5-4 = 1 * 1/2 = 0.5?

Answer 55

you mean .5*(5-3)

Answer 56

I suck :P.

Answer 57

no no you don't

Answer 58

so 1? :P I'm just not thinking, doing this too fast.

Answer 59

yea man that is right!

Answer 60

Ok sweetness. So I can still use the old method and just switch back to X's(I feel more comfortable that way than changing the limits and all that jazz) :) Onto the next question!

Answer 61

Alright...just keep practicing and check yourself....
It is the best way to learn these...
I mean that is what worked for me...
I did like easy, medium, and hard looking problems and I did them til I felt comfortable
But make sure you are doing it the right way
And the way to do that is to make sure you are getting the right answer each time
Usually I do the odd ones and check myself with the back of the book
And do some dirty looking even ones when I feel comfortable with the dirty looking odd ones

Answer 62

Good luck