Home › Mathematics › Pls Integrate (1-X^1/2)^2/X^1/2 Dx?
thank you so much!
-Anonymous
First square out the top:
(1-x^1/2)^2=1-2(x^(1/2))+[x^(1/2)]^2
=1-2x^(1/2)+x
Now divide each term by x^(1/2):
x^(-1/2) - 2 +x^(1/2) and
integrate term by term giving
2x^(1/2) - 2x+(2/3)x^(3/2) + constant
NB Integral of x^n=(1/(n+1))x^(n+1) as long as
n is not -1. n can be fractional, negative etc.
-Anonymous
(1-x^1/2)^2=1-2(x^(1/2))+[x^(1/2)]^2
=1-2x^(1/2)+x
Now divide each term by x^(1/2):
x^(-1/2) - 2 +x^(1/2) and
integrate term by term giving
2x^(1/2) - 2x+(2/3)x^(3/2) + constant
NB Integral of x^n=(1/(n+1))x^(n+1) as long as
n is not -1. n can be fractional, negative etc.
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