Substitute the limits correctly. The constant of integration is eliminated during subtraction.
INT.(-1 --> 0)[(2-x)^4]dxOriginally 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.