Substitute the limits correctly. The constant of integration is eliminated during subtraction.

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- May 19th 2006, 05:40 PMnoriveaThe definite integral
Substitute the limits correctly. The constant of integration is eliminated during subtraction.

- May 19th 2006, 06:50 PMticbolQuote:

Originally Posted by**norivea**

if u = (2-x), then du = -dx, or dx = -du.

So the original integral, in indefinite form, becomes

INT.[u^4](-du)

So, to continue,

= (-)INT.[u^4]du

= -(1/5)u^5 +C

which is, when going back away from u,

= -(1/5)(2-x)^5 +C

Now we can use the original boundaries for the definite integration,

= -(1/5)[(2-x)^5](-1 --> 0)

= -(1/5)[(2 -0)^5] -{-(1/5)[(2 -(-1))^5]}

= -(1/5)[2^5] +(1/5)[3^5]

= -(1/5)[32] +(1/5)[243]

= (1/5)[243 -32]

= (1/5)[211]

= 42.2 --------------answer.