Thread: The definite integral

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

Originally Posted by norivea

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

INT.(-1 --> 0)[(2-x)^4]dx

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.