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C4 - Integration by U substitution Q

Hi, please can someone help with this question:

Evaluate:
the integral of x [root(x+4)] dx with the limits 5,0

This is what I've done:

I let u = x+4
du/dx =1
dx=du
x=u-4

so integral of:

(u-4)(u^0.5) du

u^3/2 - 4u^0.5 du

integrated to:

2/5 u^5/2 - 8/3 u^3/2

then put x back in:

2/5(x+4)^5/2 - 8/3(x+4)^3/2

my final answer was 25.2

but the right answer is 33.73
Original post by kej817
Hi, please can someone help with this question:

Evaluate:
the integral of x [root(x+4)] dx with the limits 5,0

This is what I've done:

I let u = x+4
du/dx =1
dx=du
x=u-4

so integral of:

(u-4)(u^0.5) du

u^3/2 - 4u^0.5 du

integrated to:

2/5 u^5/2 - 8/3 u^3/2

then put x back in:

2/5(x+4)^5/2 - 8/3(x+4)^3/2

my final answer was 25.2

but the right answer is 33.73


You have done everything right apart from working out the limits correctly.

Next time can I suggest you do not put x back in at all - just change the limits.
Reply 2
Avatar for kej817
kej817
OP
5
Original post by Mr M
You have done everything right apart from working out the limits correctly.

Next time can I suggest you do not put x back in at all - just change the limits.


I don't understand how I've worked out the limits incorrectly, they were given like that for the integral in terms of x, so if i put x in correctly they should be right? I don't know how to change the limits so that they're in terms of U :frown:
Original post by kej817
I don't understand how I've worked out the limits incorrectly, they were given like that for the integral in terms of x, so if i put x in correctly they should be right? I don't know how to change the limits so that they're in terms of U :frown:


you haven't used your calculator (or brain which it was) correctly

You should have got 1265−−12815\frac{126}{5} - \frac{-128}{15} if it helps.

Regarding your other question, if u = x + 4 and x = 0 or 5 what does u = ?
Reply 4
Avatar for kej817
kej817
OP
5
ah i forgot to sub in x=0, I've got into the habit of ignoring it when its a limit because...well I usually can...>.< as if I spent over an hour looking at it and thats all it was. Thanks for your help :smile:
Original post by kej817
ah i forgot to sub in x=0, I've got into the habit of ignoring it when its a limit because...well I usually can...>.< as if I spent over an hour looking at it and thats all it was. Thanks for your help :smile:


You are welcome.

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