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C4 question watch

1. I've been doing C 4 past papers and two similar questions have come up and I'm sure there'll be more, however I can only do half the question.

They're the same style question and I'm fine with both first questions, but for the second party I'm absolutely stumped.
Any hints?
2. (Original post by eggfriedrice)
I've been doing C 4 past papers and two similar questions have come up and I'm sure there'll be more, however I can only do half the question.

They're the same style question and I'm fine with both first questions, but for the second party I'm absolutely stumped.
Any hints?
For each Q, use the transformation in the first part by working out the new limits from the substitution. This should be obvious
3. (Original post by eggfriedrice)
I've been doing C 4 past papers and two similar questions have come up and I'm sure there'll be more, however I can only do half the question.

They're the same style question and I'm fine with both first questions, but for the second party I'm absolutely stumped.
Any hints?
The most important part of definite integral substitutions is to change the limits.
4. (Original post by eggfriedrice)
I've been doing C 4 past papers and two similar questions have come up and I'm sure there'll be more, however I can only do half the question.

They're the same style question and I'm fine with both first questions, but for the second party I'm absolutely stumped.
Any hints?
Why don't you sub in "u".
Then work out du/dx, and sub in what you need to replace dx.

Then mess around with the integral to get it in the form you need.
Why don't you sub in "u".
Then work out du/dx, and sub in what you need to replace dx.

Then mess around with the integral to get it in the form you need.
She says its the second part she can't do . . .
6. (Original post by Indeterminate)
For each Q, use the transformation in the first part by working out the new limits from the substitution. This should be obvious

(Original post by joostan)
The most important part of definite integral substitutions is to change the limits.
Still got me lost ):
7. (Original post by eggfriedrice)
Still got me lost ):
The limits are still the x values. You have to use the substitutions in first parts to get the limits corresponding to u and theta
8. (Original post by eggfriedrice)
Still got me lost ):
As Indeterminate says, you've already transformed the integral.
You sub in the x values to get out the value and change the limits. You then evaluate this new integral to get what it is you want
9. (Original post by joostan)
She says its the second part she can't do . . .
Can't she just integrate what she found (the u integral) and use NEW LIMITS by subbing into u=e^x+1.

And then sub back u=e^x+1 into the answer????

Sorry I did this stuff like 3 years ago, so I vaguely remember it.
Can't she just integrate what she found (the u integral) and use NEW LIMITS by subbing into u=e^x+1.

And then sub back u=e^x+1 into the answer????

Sorry I did this stuff like 3 years ago, so I vaguely remember it.
If you use the new limits, you don't convert the integral back into terms with x's in.
11. So you can do part a). For b), use the bit you've worked out as the integral. But you need to change the limits, as the limits give in the question are for an integral in terms of x. To change the limits, put each limit into the substitution equation...
a) u=e^x +1, u=e^1 +1 and u=e^0 +1, so the new limits are u=e+1 and u=1
b) x=sin^2(theta), 1=sin^2(theta) and 0=sin^2(theta), sin(theta)=1 and sin(theta)=0, so the new limits are 90 and 0.
Put the new limits into your equation from part one and then integrate as usual
12. (Original post by joostan)
If you use the new limits, you don't convert the integral back into terms with x's in.
For 6) ii) you do.
13. Ok I think I've done it now. Well all I did was integrate the transformation then subbed in the values. However I got e +1-ln(e +1/2) rather than e- 1-ln(e+1/2) :s
I'm going to try the other one and see if it works out doing the same method.
14. (Original post by Voyageuse)
So you can do part a). For b), use the bit you've worked out as the integral. But you need to change the limits, as the limits give in the question are for an integral in terms of x. To change the limits, put each limit into the substitution equation...
a) u=e^x +1, u=e^1 +1 and u=e^0 +1, so the new limits are u=e+1 and u=1
b) x=sin^2(theta), 1=sin^2(theta) and 0=sin^2(theta), sin(theta)=1 and sin(theta)=0, so the new limits are 90 and 0.
Put the new limits into your equation from part one and then integrate as usual
Ah I didn't change the limits, thanks! I'll try again and see what I'll get.

Also wouldn't u be =e +1 and =2 ?
For 6) ii) you do.
Not if you convert the x-limits into the theta limits then integrate with respect to theta . . .
16. Also wouldn't u be =e +1 and =2 ?[/QUOTE]
Yeah, you're right - sorry, my mistake!
17. (Original post by joostan)
Not if you convert the x-limits into the theta limits then integrate with respect to theta . . .
lol the top question.
18. (Original post by joostan)
Not if you convert the x-limits into the theta limits then integrate with respect to theta . . .
Are you doing A levels now?
19. (Original post by Voyageuse)
Also wouldn't u be =e +1 and =2 ?
Yeah, you're right - sorry, my mistake![/QUOTE]

Thanks! I've done it now. it's a lot simpler than it seems, thanks for your help!
20. Woo hoo! Success! No worries and well done

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