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# C3 Integration by substitution problem watch

1. Hi everyone,

We have just finished the calculus part of c3 today and my teacher set us some challenging problems, ive done 7/8 but cant seem to get the last one right, it is...

Int [sin(x).cos^3(x)] dx from 0 to pi/6

I let u = sinx

du/dx = cosx , dx/du = 1/cosx

rearranged the integral into,

Int [sinx.cosx.(1-sin^2(x))] dx

subbed in u and dx/du , the cosines cancel, and were left with

Int [ u - u^3 ] du from 0 to pi/6

after putting the values in, to the integral i get,

7/64

the answers say it should be 6/13
ive checked my work a few times now cant seem to find any mistakes, could some one please show me the way to do this, or show me my error, thank you in advance =]
2. (Original post by cj_134)
Hi everyone,

We have just finished the calculus part of c3 today and my teacher set us some challenging problems, ive done 7/8 but cant seem to get the last one right, it is...

Int [sin(x).cos^3(x)] dx from 0 to pi/6

I let u = sinx

du/dx = cosx , dx/du = 1/cosx

rearranged the integral into,

Int [sinx.cosx.(1-sin^2(x))] dx

subbed in u and dx/du , the cosines cancel, and were left with

Int [ u - u^3 ] du from 0 to pi/6

after putting the values in, to the integral i get,

7/64

the answers say it should be 6/13
ive checked my work a few times now cant seem to find any mistakes, could some one please show me the way to do this, or show me my error, thank you in advance =]
Need to remember to change the limits to terms of u. Either that or replace any u's with sin x before you evaluate using the limits.
3. (Original post by JamesyB)
Need to remember to change the limits to terms of u. Either that or replace any u's with sin x before you evaluate using the limits.
I did replace all the u's with sinx before entering the limits, and i got 7/64
4. I got 7/64?
5. I get 7/64 as well, so I reckon the answer in the book is wrong.
6. Oh ok then, yea might be a wrong answer then =s
7. (Original post by cj_134)
Oh ok then, yea might be a wrong answer then =s
You'd be surprised at the number of errors in text books...
8. (Original post by JamesyB)
You'd be surprised at the number of errors in text books...
Yea thats pretty lame, since i've spent quite a while going over this question because I though I made a mistake

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