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Integration. XD C4

Matthew2010

Hi,

Is this correct? :s-smilie:

Find the integral of xcos2x dx:

xsin2x / 2 - cos2x / 4 + c

Use the result above to find x cos^2(x) dx:

So far I got:

integral x [2cos^2(x) - 1] dx

integral 2x cos^2(x) - x dx

2integral x cos^2(x) - integral x dx...

Is this correct atm, also where do I go from here? :s-smilie:

Thanks!

Reply 1

vc94

The identity cos(2A) = 2cos^2(A) - 1, rearrange gives cos^2(A) = (1 + cos(2A))/2

So integral of xcos^2(x) = integral of x*(1 + cos(2x))/2
so you can use your previous result.

Reply 2

Matthew2010

Original post by vc94

The identity cos(2A) = 2cos^2(A) - 1, rearrange gives cos^2(A) = (1 + cos(2A))/2

So integral of xcos^2(x) = integral of x*(1 + cos(2x))/2
so you can use your previous result.

Thank you very much. Ive been seeing this a lot where part b is the same answer as part a. You just have to find out how to get there in relation with the previous part.