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# Problems with u-sub core 4. watch

1. I am having problems doing problems when I am given a u as in a form u^2 = this and that.

If I were to pick my own value, I'd usually just pick "u", even if it's rooted. But whenever I have to take it squared, or u rooted, I encounter problems.

Usually I just integrate, and then substitute for dx.

With u^2's I get really confused.

For example, in c4, exercise 6H number 4.

I am given x√(2-x) dx

There needs to be an EXACT value to be found, and all that has to be integrated with limits from 2 to 0.

While I did took u as a 2-x, I could only find the approximate value, while when looking at the worked answer, it was suggested I take u^2. I would have never though of that.. and I am struggling in knowing when to take u^2 or rooted u or normal u.

Because by taking u^2, you'd end up with a surd fraction, and it will also make you change limits with one of them being root 2.

So yeah.. I am really having troubles with these... any advice from someone who is good or has experienced the same thing?
2. (Original post by studentFlipper)
I am having problems doing problems when I am given a u as in a form u^2 = this and that.

If I were to pick my own value, I'd usually just pick "u", even if it's rooted. But whenever I have to take it squared, or u rooted, I encounter problems.

Usually I just integrate, and then substitute for dx.

With u^2's I get really confused.

For example, in c4, exercise 6H number 4.

I am given x√(2-x) dx

There needs to be an EXACT value to be found, and all that has to be integrated with limits from 2 to 0.

While I did took u as a 2-x, I could only find the approximate value, while when looking at the worked answer, it was suggested I take u^2. I would have never though of that.. and I am struggling in knowing when to take u^2 or rooted u or normal u.

Because by taking u^2, you'd end up with a surd fraction, and it will also make you change limits with one of them being root 2.

So yeah.. I am really having troubles with these... any advice from someone who is good or has experienced the same thing?
What was wrong with ? It's the same substitution as , and you'll go through the same motions to evaluate the integral. Would you mind posting your working where you try using the rather than substitution?
3. (Original post by studentFlipper)
I am having problems doing problems when I am given a u as in a form u^2 = this and that.

If I were to pick my own value, I'd usually just pick "u", even if it's rooted. But whenever I have to take it squared, or u rooted, I encounter problems.

Usually I just integrate, and then substitute for dx.

With u^2's I get really confused.

For example, in c4, exercise 6H number 4.

I am given x√(2-x) dx

There needs to be an EXACT value to be found, and all that has to be integrated with limits from 2 to 0.

While I did took u as a 2-x, I could only find the approximate value, while when looking at the worked answer, it was suggested I take u^2. I would have never though of that.. and I am struggling in knowing when to take u^2 or rooted u or normal u.

Because by taking u^2, you'd end up with a surd fraction, and it will also make you change limits with one of them being root 2.

So yeah.. I am really having troubles with these... any advice from someone who is good or has experienced the same thing?
I just did this with u=2-x
Why would you get an approximate answer?

The limits change from 0,2 to 2,0 and you have some square roots of u
So the answer is a multiple of root2
4. (Original post by studentFlipper)
<snip>
(To link between my answer and TenOfThem's, usually more than one substitution will work.)
5. (Original post by Smaug123)
What was wrong with ? It's the same substitution as , and you'll go through the same motions to evaluate the integral. Would you mind posting your working where you try using the rather than substitution?
(Original post by TenOfThem)
I just did this with u=2-x
Why would you get an approximate answer?

The limits change from 0,2 to 2,0 and you have some square roots of u
So the answer is a multiple of root2

Well for me it's not that easy taking u^2, it does confuse me. I am really struggling with math, and sometimes I spent hours staring at a problem or even at a worked out example without really understanding.

Anyway, I drew the worked example of taking 2-x as a u, but I probably messed up with signs on the way or broke some rules.
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6. (Original post by studentFlipper)
Well for me it's not that easy taking u^2, it does confuse me. I am really struggling with math, and sometimes I spent hours staring at a problem or even at a worked out example without really understanding.

Anyway, I drew the worked example of taking 2-x as a u, but I probably messed up with signs on the way or broke some rules.
I haven't checked your working, but why have you converted everything to decimals?

You should know that

and similarly

so you can write everything as a multiple of

(also your notation is slightly wrong - you should have written dx = -du not dx = -1 so that your 'u integral' ends with -du instead of -1. Always make it clear what you're integrating with respect to)
7. (Original post by studentFlipper)
Well for me it's not that easy taking u^2, it does confuse me. I am really struggling with math, and sometimes I spent hours staring at a problem or even at a worked out example without really understanding.

Anyway, I drew the worked example of taking 2-x as a u, but I probably messed up with signs on the way or broke some rules.
As I said you have everything in root2s

Do not change to decimal
8. (Original post by studentFlipper)
Well for me it's not that easy taking u^2, it does confuse me. I am really struggling with math, and sometimes I spent hours staring at a problem or even at a worked out example without really understanding.

Anyway, I drew the worked example of taking 2-x as a u, but I probably messed up with signs on the way or broke some rules.
So the substitution is essentially identical:
differentiating both sides of that expression by the chain rule, , so and the integral becomes .

This is a polynomial expression of so it's easy to evaluate.
9. (Original post by Smaug123)
So the substitution is essentially identical:
differentiating both sides of that expression by the chain rule, , so and the integral becomes .

This is a polynomial expression of so it's easy to evaluate.

Aagghhh it's too complicated for me, I don't understand it. I know the essence of the chain rule,. I just don't see how it is applicable here, I can't get my head around it. I see that you differentiated both sides u^2 >> 2u and 2 - x >>> -1 but why you would multiply 2u by 2u/dx or why do we need a negative dx is what I don't get either. Usually when I am doing integrals like these, I am solving for dx or dt, and then plugging it into the integral. Even considering I do all that, I am still somewhat confused with how we got root 2 in there, this is all so complicated for me when it should be easy.
(Original post by TenOfThem)
As I said you have everything in root2s

Trying to grasp my head around it, too problematic to understand. I have everything in root of 2 as in my u's because they are rooted? You mean like turn 2u^3/2 into something like 2u times *root* u?

Do not change to decimal
(Original post by davros)
I haven't checked your working, but why have you converted everything to decimals?

You should know that

and similarly

so you can write everything as a multiple of

(also your notation is slightly wrong - you should have written dx = -du not dx = -1 so that your 'u integral' ends with -du instead of -1. Always make it clear what you're integrating with respect to)

Yes you are right! I should have used 1*(-du) instead. I'll try to remember that, I also know the powers multiplication conversion. The problem for is, that I think I wouldn't have thought of changing them to the roots in the first place, even when asked to give an exact value. I just wouldn't have thought of it. I don't know what I need, maybe mass practice... but as soon as I get to review exercises I forget half the stuff I tried to learn haha
10. (Original post by studentFlipper)
Aagghhh it's too complicated for me, I don't understand it. I know the essence of the chain rule,. I just don't see how it is applicable here, I can't get my head around it. I see that you differentiated both sides u^2 >> 2u and 2 - x >>> -1 but why you would multiply 2u by 2u/dx or why do we need a negative dx is what I don't get either. Usually when I am doing integrals like these, I am solving for dx or dt, and then plugging it into the integral. Even considering I do all that, I am still somewhat confused with how we got root 2 in there, this is all so complicated for me when it should be easy.
. That's the chain rule. The negative dx doesn't mean anything - I just lazily didn't multiply through by -1 to give us a expression.

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