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Integration Questions (2)

I need a bit of help on these integration questions.



Can someone just outline the steps especially for the 2nd question please
Reply 1
You'll get the most benefit out of the questions if you attempt to find the solution steps yourself. Often the biggest hurdle in solving a problem is working out what to do; the execution is straightforward.
Reply 2
I understand the first part as to simplify:

(2-x)x^1/2
but do I multiply both 2-x by the x^1/2 or just the x in the bracket, once I know that I can do it.
Reply 3
Original post by LifeIsGood

Original post by LifeIsGood
I understand the first part as to simplify:

(2-x)x^1/2
but do I multiply both 2-x by the x^1/2 or just the x in the bracket, once I know that I can do it.


The usual rules for brackets apply: (2x)x1/2=2x1/2xx1/2(2-x)x^{1/2} = 2x^{1/2} - xx^{1/2}
note that (f(x)+g(x))dx=(f(x))dx+(g(x))dx\int(f(x)+g(x)) dx = \int(f(x))dx + \int(g(x))dx

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