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    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 =]
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    (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.
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    (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
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    I got 7/64?
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    I get 7/64 as well, so I reckon the answer in the book is wrong.
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    Oh ok then, yea might be a wrong answer then =s
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    (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...
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    (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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Updated: September 27, 2010
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