Math Is Fun Forum

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

questions from integration

Q.1.

find a,b,c,d and f.

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friendship is tan 90°.

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: questions from integration

Integrate the left side. Simplify it. The result should be equal to the expression on the right.
Or backward - differentiate the right side, the result should be equal to the expression under the integral.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: questions from integration

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: questions from integration

I tried integrating left or differentiating right but it became lengthy.
bobbym, what's EM method?

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friendship is tan 90°.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: questions from integration

Hi;

That is an acronym for Experimental Mathematics.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: questions from integration

Let u = sin(x) and express sin(3x) in terms of sin.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: questions from integration

My earlier suggestion didn't, work, sorry.

But this does.

Start with the right hand side and differentiate chiefly using the product rule.

Use zetafunc`s suggestion to express sin(3x) in terms of sin(x) and sin cubed.

Now make the left hand side look like the right hand side.

You can quickly determine a to start off the sin cubed term and b to avoid any sin squared (remember sin squared + cos squared).

Then fix c to finalise the sin3x and sin x terms.

Then d and f allow you to tidy up the rest.

Bob

Last edited by Bob (2015-08-31 04:08:42)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: questions from integration

yes I solved it now. Thanks.

here comes another question:-

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friendship is tan 90°.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: questions from integration

Was post #3 the official answer?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: questions from integration

yes I solved it now. Thanks.

here comes another question:-

I posted a video solution to your problem here: https://www.youtube.com/watch?v=CCEq3ylr1OE

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: questions from integration

hi zetafunc,

Beautiful solution!  And nicely explained.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: questions from integration

thanks. It was really very well explained.
well what are the things that should come in our mind for making substitution when we encounter such problems?

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friendship is tan 90°.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: questions from integration

Normally with these types of problems, in which you've got a function nested within another function (e.g. log(sin(x)), e^(tan(x)), arctan(sec(x) + cos(x))), what they expect you to do is to make the most obvious substitution -- in this case, whatever the function inside arctan() was.