Integrate x/18(6-x) from 0 to 6. Please show some working as I cannot do this whichever way I try.
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The Music Roob Ninja
ANSWERS: 1
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Did you mean x/(18(6-x)) ? (A) or (x/18)(6-x) ? (B) You MUST use more brackets when you use '/'. How to do A: Ignore the factor of 18 for now. You have x/(6-x) Now need to do a "long division". (This is called "partial fractions"). The highest powers of x in the numerator and denominator are x and -x. IF you divde these you get -1 So -1 is part of the divisor. -1 times (6-x) is x-6 but the numerator is x so need to add 6/(6-x) to make up x/(6-x) Now the powers of x in the numerator are less than the denominator, so stop dividing: Now the formula is -1 + 6/(6-x) Use change of variable t=6-x to integrate this. How to do B: Just multiply it out and integrate each term separately.
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