Math Is Fun Forum

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

integration trouble

question from textbook, i can do first 3 sections, but im lost on 4th part

My workings for parts a through c

But I'm lost on how to do part d

Last edited by luca-deltodesco (2008-03-13 03:40:32)

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: integration trouble

Note: I was trying to write out the whole problem but somehow Latex doesnt seem to work. I must be dumb. This always happens to me. Can anyone point out thats wrong?

Last edited by LuisRodg (2008-03-13 08:40:02)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: integration trouble

the problem is that you are starting a new line with nothing there. note how ive formatted it with the \\ for new line. even having a blank line below the math tag before the first line of latex gives an error

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: integration trouble

For part d:

Plug this in a calculator and it gives you = 0.159435246248

Does this answer part d or I missed something?

Last edited by LuisRodg (2008-03-13 08:53:32)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: integration trouble

The answer given is

which doing in calculator is 0.15943524624841969940982813598718

so that's right then. i never knew you could do a substitution like that, ive only ever used a substitution in the format u = f(x), find du/dx. divide du/dx from the integral, change the limits. i.e. example

so in the end we have:

which is what i get when plugging it into wolfram's integrator

Last edited by luca-deltodesco (2008-03-13 08:57:23)

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: integration trouble

Yes. That is called "trigonometric substitution" which is used in integrals that have square roots in it which otherwise would be impossible to do, or way harder.

Part c could have been done with the same trig substitution.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: integration trouble

well where im up to in the course ive covered many trig substitution, i was referring to the explicit manner of substitution. having the variable as a function of another, and finding as you did dx = f(y)dy and substituting that directly without having to change the limits

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: integration trouble

My professor always tells us to change the limits but for me its more work and I never do it. Besides, I have gotten a couple questions on tests wrong because I changed the limits of integration where I couldnt because of sin, cos etc. And to be honest, I really cant tell where I can change the limits or not, so I never change them and plug them in when I have converted the answer back to x (or the initial variable). Works out for me.

Last edited by LuisRodg (2008-03-13 09:01:51)