# Thread: Integration By Parts

1. ## Integration By Parts

I am doing integration by parts and am struggling a little bit with two revision questions:

The first is:

1) \int cos(2x).(5x+1).dx

The answer I have is - (5x+1)sin2x/2+5/4cos2x

Is this right although I am not sure how I got there.

The other question is a Definite Integral:

2) \int (x+2)sinx.dx and the limits are 1 and 2

I just can't seem to get the right indefinite integral to be able to replace x with the limits.

The answer I get is (x+2)(-cos(x))+sin(x) but when O replace x with the upper and lower limit I get the wrong answer.

Can anyone please help me.

Thanks

M

2. 1) is correct. Will post a pic to show how.

2) Are you subtracting cos x, there, or... should there be brackets...?

1) Just in case a picture helps... ... where (key in spoiler) ...

Spoiler: ... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x. And, ... is lazy integration by parts, doing without u and v.

2) is much the same... you try. _________________________________________

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3. OK, you've now put the brackets in... is that not working?

Again, just in case... (And follow the key in post 2.)

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

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4. Thank you that makes sense. Are you also able to help me with the following as well?

∫(7-x)sin(x).dx

I know the answer is:

(x-7).cos(x)-sin(x)

but i can't figure out why the (7-x) is swapped over and becomes (x-7).

M

5. (x - 7) = - (7 - x)

The negative belonged originally to the cos (but then to the whole product). I.e. it's just a neat way of removing the negative.

We could balloonify it as either... ... or... _________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!

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