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c4 maths

can someone help me with this question?

∫( 4 − x^2)^0.5 dx

x = 2 sinx

limits are 1 and 0
(edited 7 years ago)
What does the 'x = 2 sinx' refer to?
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619-booyaka
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Original post by rebirth61213
What does the 'x = 2 sinx' refer to?

you have to sub x into the equation as 2sinx
Original post by 619-booyaka
can someone help me with this question?

∫( 4 − x^2)^0.5 dx

x = 2 sinx

limits are 1 and 0


Do it like any other substitution. Do not forget the limits.
(2sinx)^2 = 4*(sinx)^2

(sinx)^2 = 1 - (cosx)^2

Sub that in (I'll leave the rest to you; you should end up with a simple function to integrate).
(edited 7 years ago)
Original post by ODES_PDES
Do it like any other substitution. Do not forget the limits.


I don't think he/she meant that this is a 'u-substitution method' question. (why would one want to sub in 2sinx?) I think he/she meant that the x in the above expression is 2sinx and avoided putting that in the top expression in order to maintain clarity (I think).
Original post by rebirth61213
I don't think he/she meant that this is a 'u-substitution method' question. (why would one want to sub in 2sinx?) I think he/she meant that the x in the above expression is 2sinx and avoided putting that in the top expression in order to maintain clarity (I think).


Take over as I am rusty:tongue:
Original post by 619-booyaka
can someone help me with this question?

∫( 4 − x^2)^0.5 dx

x = 2 sinx

limits are 1 and 0


Original post by rebirth61213
I don't think he/she meant that this is a 'u-substitution method' question. (why would one want to sub in 2sinx?) I think he/she meant that the x in the above expression is 2sinx and avoided putting that in the top expression in order to maintain clarity (I think).


Maths professors at uni would be ripping their hair out at the line x=2sinx, even if it's just to make representing things easier - there are 25 other letters to choose from! But really, it doesn't matter at this stage :tongue:
arcsin(x/2)=x

∫( 4 − arcsin(x/2)^2)^0.5 dx

there I solved it.

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