Easy Integration :( (1 Viewer)

[12o9]

Hey guys, sorry about this, but for some reason I can't remember how to integrate √(25-x²)

Thanks in advance.
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[tommykins]

let x = 5sin@

if it's a definite integral, note that its a semi circle.

 

[Aerath]

Are we supposed to know that for 2U?

 

[shaon0]

S sqrt(25-x^2)
= 1/2 sqrt(25-x^2)*x + 25/2 arcsin (x/5)
.....i think its the answer.
I'll try to scan you my solution.

 

[Just.Snaz]

Hey guys, sorry about this, but for some reason I can't remember how to integrate √(25-x²)

Thanks in advance.

Umm.. I think that requires substitution which is actually then 3 unit and if they haven't given you wat to sub in for what then it's 4 unit.

I would do

let x = 5 sin@
dx = 5cos@ d@

integral (25 - 25 sin²@)^(1/2) .5 cos@ d@
= integ [25(1 - sin²@)]^(1/2) .5 cos@ d@
= integ 5cos@ .5cos@ d@
= integ 25 cos²@ d@
and cos2@ = 2cos²@ - 1 (3 unit double the angle)
therefore, cos²@ = 1/2 (cos2@ + 1)

so integ. 25/2 [cos2@ + 1] d@
= 25/4(sin2@ + @) + C

 

[tommykins]

Are we supposed to know that for 2U?

Don't think so..normally if they give you an integral like that, it's a definite integral

ie. int sqrt(a^2-x^2) dx a->0

 

[tommykins]

Umm.. I think that requires substitution which is actually then 3 unit and if they haven't given you wat to sub in for what then it's 4 unit.

I would do

let x = 5 sin@
dx = 5cos@ d@

integral (25 - 25 sin²@)^(1/2) .5 cos@ d@
= integ [25(1 - sin²@)]^(1/2) .5 cos@ d@
= integ 5cos@ .5cos@ d@
= integ 25 cos²@ d@
and cos2@ = 2cos²@ - 1 (3 unit double the angle)
therefore, cos²@ = 1/2 (cos2@ + 1)

so integ. 25/2 [cos2@ + 1] d@
= 25/4(sin2@ + @) + C

Not entirely correct. It's also 25/2[sin2@/2 + @] , not 25/4.

You need to revert the @'s back into x's.

 

[tacogym27101990]

nah the only way theyd ask you that is if it had the limits -5 >5 or 0>5
so you can just do the area of a semi circle or quarter circle

 

[lyounamu]

Hey guys, sorry about this, but for some reason I can't remember how to integrate √(25-x²)

Thanks in advance.
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I would actually find the area of the semi-circle with raidus of 5 for that question.

A = 1/2 x 5^2 x pi

 

[Aerath]

I would actually find the area of the semi-circle with raidus of 5 for that question.

A = 1/2 x 5^2 x pi

It's not a definite integral, though.

 

[lyounamu]

It's not a definite integral, though.

Yeah, I know. I actually used the method that tommy suggested.

But I used my method to check it.

 

[12o9]

Whoa. You guys are awesome . Thanks for the help.

 

[shaon0]

Whoa. You guys are awesome . Thanks for the help.

sorry, my solution is not scanning for some reason ....sorry

 

[lyounamu]

sorry, my solution is not scanning for some reason ....sorry

Your method won't work anyway.

 

[shaon0]

Your method won't work anyway.

my method? Is my answer wrong?

 

[lyounamu]

my method? Is my answer wrong?

Yeah and your method was wrong from the start. You cannot use that method because you can only use that when the equation is in the form (ax+b)^something.

This is a 3-Unit HSC level question where you have to let u = sin x or whatever to get it right.

 

[shaon0]

Yeah and your method was wrong from the start. You cannot use that method because you can only use that when the equation is in the form (ax+b)^something.

This is a 3-Unit HSC level question where you have to let u = sin x or whatever to get it right.

...so my answer is wrong. I'll try again. Sorry

 

[lolokay]

Yeah and your method was wrong from the start. You cannot use that method because you can only use that when the equation is in the form (ax+b)^something.

This is a 3-Unit HSC level question where you have to let u = sin x or whatever to get it right.

what was wrong with his answer?

 

[shaon0]

Yeah and your method was wrong from the start. You cannot use that method because you can only use that when the equation is in the form (ax+b)^something.

This is a 3-Unit HSC level question where you have to let u = sin x or whatever to get it right.

I can't find my fault, i kept trying. I can't post my answer since it takes to long to write on computer. and i am doing my physics assignment.

 

[tommykins]

shaon0's working is correct.