Inverse Trig Integration Question (1 Viewer)

[rand_althor]

Hey how would you do this question without using substitution?

 

[integral95]

 

[integral95]

You'll eventually get that answer if you use the substitution u = (x-b)

 

[VBN2470]

. Just recognise that it is in the form as a standard inverse sine integral, but recognising this still (implicitly) requires the substitution .

EDIT: Just realised I got beaten above

 

[rand_althor]

Okay thanks guys!

 

[Drsoccerball]

Try this to make sure youve got it

 

[SpiralFlex]

^With conditions

 

[rand_althor]

Is the answer ?

 

[rand_althor]

^With conditions

Are the conditions for the integral or the inverse sine function?

 

[InteGrand]

Are the conditions for the integral or the inverse sine function?

Conditions such as: c > 0, and we assume a is positive in your answer (we should actually write |a| strictly speaking, but this is kind of nitpicking).

 

[rand_althor]

Conditions such as: c > 0, and we assume a is positive in your answer (we should actually write |a| strictly speaking, but this is kind of nitpicking).

So that's for the inverse sine function?

What is the domain of the inverse sine function?

 

[InteGrand]

So that's for the inverse sine function?

What is the domain of the inverse sine function?

I was talking about for the integral.

For example, if c < 0, we would end up with something like this:

(for example).

There, the expression under the square root in the integrand is negative, and we don't deal with these situations in the HSC.

And the domain of is .

 

[rand_althor]

Ah okay, that makes sense.

Sorry I meant the domain of

 

[InteGrand]

Ah okay, that makes sense.

Sorry I meant the domain of

Domain of that is (assuming c > 0) .

This can be simplified to isolate x in the middle, which is probably what you wanted (just make sure you're careful to flip inequality signs if you multiply through by negative numbers).

 

[rand_althor]

If we assume that a > 0, would we need to take two cases for r? I.e r > 0 and r < 0 ?

 

[InteGrand]

If we assume that a > 0, would we need to take two cases for r? I.e r > 0 and r < 0 ?

Pretty much, yes.

 

[rand_althor]

Thanks for the help!