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Math 32....how was it? :/

ffaadyy

ffaadyy

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beststriker said:
can anyone solve the volume ques plz??
Click to expand...

y = x^(1/2) ln x

Volume = pie ( y )^2
Volume = pie [ x^(1/2) ln x ]^2
Volume = pie [x (ln x)^2]

Now use integration by parts to integrate 'x (ln x)^2'

x (ln x)^2
(x^2/2)(ln x)^2 - [x^2 /2 * 2 ln x * 1/x]
(x^2/2)(ln x)^2 - [x ln x]

Now integrate 'x ln x'

x ln x
(x^2/2) ln x - [x^2/2 * 1 /x]
(x^2/2) ln x - [x/2 ]
(x^2/2) ln x - x^2/4

(x^2/2)(ln x)^2 - [x ln x]
(x^2/2)(ln x)^2 - [ (x^2/2) ln x - x^2/4 ]
(x^2/2)(ln x)^2 - (x^2/2) ln x + x^2/4

Now put the limits 'e' (upper) and '1' (lower).

Volume = pie [(e^2/2)(ln e)^2 - (e^2/2) ln e + e^2/4] - [(1^2/2)(ln 1)^2 - (1^2/2) ln 1 + 1^2/4 ]
Volume = pie [(e^2/2) - (e^2/2) + e^2/4] - [ 1/4 ]
Volume = pie [e^2/4] - [ 1/4 ]
Volume = (pie/4)(e^2 - 1)

Therefore, the volume is '(pie/4)(e^2 - 1)'.
 
beststriker

beststriker

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ffaadyy said:
y = x^(1/2) ln x

Volume = pie ( y )^2
Volume = pie [ x^(1/2) ln x ]^2
Volume = pie [x (ln x)^2]

Now use integration by parts to integrate 'x (ln x)^2'

x (ln x)^2
(x^2/2)(ln x)^2 - [x^2 /2 * 2 ln x * 1/x]
(x^2/2)(ln x)^2 - [x ln x]

Now integrate 'x ln x'

x ln x
(x^2/2) ln x - [x^2/2 * 1 /x]
(x^2/2) ln x - [x/2 ]
(x^2/2) ln x - x^2/4

(x^2/2)(ln x)^2 - [x ln x]
(x^2/2)(ln x)^2 - [ (x^2/2) ln x - x^2/4 ]
(x^2/2)(ln x)^2 - (x^2/2) ln x + x^2/4

Now put the limits 'e' (upper) and '1' (lower).

Volume = pie [(e^2/2)(ln e)^2 - (e^2/2) ln e + e^2/4] - [(1^2/2)(ln 1)^2 - (1^2/2) ln 1 + 1^2/4 ]
Volume = pie [(e^2/2) - (e^2/2) + e^2/4] - [ 1/4 ]
Volume = pie [e^2/4] - [ 1/4 ]
Volume = (pie/4)(e^2 - 1)

Therefore, the volume is '(pie/4)(e^2 - 1)'.
Click to expand...
i got the formula and the expression right, but messed up with the integration of (ln x)^2. and then completed the ques with the wrong integral. :(
will i get some marks??
 
M

mukki

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Saiyan said:
That's right! 68 is roughly 91% so its an A* but still you have to score good marks in the other papers. For me I flunked my P1 exam last year but still managed to get a 91% because of my brilliant S1 exam. So A* is actually achieved with both the AS and A2 exams.
Click to expand...
im giving accel maths actually p1 il manage 74 and m1 il manage 46 .. s1 is hard for me though :)
 
A

AGEG

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If on the differential equation question I integrated the right hand side incorrectly as '2e^2x' instead of '1/2 e^2x' however did all the steps correctly, would I get error carried forward? and if not/so how many marks would I lose?

Jazak Allah Khair.
 
ffaadyy

ffaadyy

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AGEG said:
If on the differential equation question I integrated the right hand side incorrectly as '2e^2x' instead of '1/2 e^2x' however did all the steps correctly, would I get error carried forward? and if not/so how many marks would I lose?

Jazak Allah Khair.
Click to expand...

You actually differentiated 'e^2x' instead of integrating it. I have no idea about how many marks you'll get as even the method isn't correct.
 
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Saiyan

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ffaadyy said:
Do you remember that question? What was it?
Click to expand...

The equation of a curve is y=3sinx+4cos^3x
(i) Find the x-co-ordinates of the stationary points in the interval 0<x<pie. [6]
(ii) Determine the nature of the stationary point in this interval for which x is least. [2]
 
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