Integration qn

Yaimster SG

Integration through the use of our own substitution is no longer in the H2 Maths syllabus. They would give you explicit hints to solve for that.

So definately integration by parts for me Mr. Green

HyuugaNeji SG

I dont think you can solve this question by integration by parts.

eagle SG

tamago has done it using by parts

check above posts

HyuugaNeji SG

thanks...nowsaday my maths kns already.

tanjun SG

lol. The by parts method is really unexpected.

Try this question. Very interesting too. Have to use tamago method to solve it.

eagle SG

i forgot how already, but I think if you use complex numbers, you can solve it too........ you do the by parts, I do the complex numbers, then compare answer?

edit: I used complex numbers (euler's formula) to solve, my final answer is

1/2 e^x (cos x + sin x) Wink

Differentiating it gives you the answer above, so I'm pretty sure it is correct. I shall now type it out on MS word, and post a screenshot of it here

^tamago^ SG

thanks in advance, eagle. Embarassed

HyuugaNeji SG

recursive formula ba... cos integrate or differentiate e^x always e^x.

so just take
INT e^x(cos x) =e^x(cos x) - INT e^x(-sin x)
=e^x(cos x) + INT e^x(sin x)
=e^x(cos x) + e^x(sin x) - INT e^x(cos x)

so 2 INT e^x (cos x) = e^x(cos x + sin x). then divide by 2.

eagle SG

Yep, this is another way Very Happy
And it should be the way to do for A levels

Anyway, for those who want to see the complex number way, here it is:

teraexa SG

This question or something similar came out for the ACJC prelims.

tanjun SG

My teacher mentioned about this trick last time of by parts to solve this type of questions. And my ans is the same as yours. Laughing

HyuugaNeji SG

what program do you people use to get the integration symbol?

eagle SG

I used MS Word

HyuugaNeji SG

wow...k

tanjun SG

MS word too. You can go to help and type integration as the helping word. If the application supports mathematical function, they will display a list of instructions to help you with them.

^tamago^ SG

tanjun can try disabling spelling checks. Embarassed

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