Extension One Revising Game (3 Viewers)
- Thread starter conics2008
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gurmies
Drover
New question:
Let x= sec@, dx=sec@tan@ d@
New question:
+c \,\, using \,\, the \,\, substitution \,\, x=\sec\theta \\\\ Hence \,\, show \,\, that \,\, \int_{2}^{3}\frac{1}{x\sqrt{x^{2}-1}}dx=\cos^{-1}(\frac{1+2\sqrt6}{6}))
I
= S (sec@tan@/(sec@sqrt((sec@)^2-1))) d@
= S d@
= @ + C
= arccos(1/x) +C
For I with limits x=3,2.
I = arccos(1/3)-arccos(1/2)
Let a=arccos(1/3), b=arccos(1/2)
I = a-b
cos(I) = cos(a-b)
cos(I) = cos(a)cos(b)+sin(a)sin(b)
cos(I) = (1/3)(1/2)+(sqrt(8)/3)(sqrt(3)/2)
cos(I) = (1/6)+sqrt(24)/6
I = arccos((1+2sqrt(6)/6)
Someone can ask a question on my behalf.
Last edited:
kurt.physics
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As no one has been able to solve Trebla problem, then (if you dont mind Trebla), for the sake of furthering the progress of this thread, i will post a new question.
given = \sin\left(\omega x + \phi \right))
where 
and 
if:
 \cos\left(\phi\right) - \sin\left(\frac{3\pi}{4}\right) \sin\left(\phi\right) = 0)
then find the value of
given
if:
then find the value of
Last edited:
addikaye03
The A-Team
Haven't attempted ii) yet but is the answer to i) k=1 and -3/2Try this:
 Find values of $k$ such that $y = e^{kx}$ satisfies this equation$\\\\$(ii) The general solution of this equation is $y = Ae^{px}+Be^{qx}$ for some constants $p$, $q$, $A$ and $B$. Find the values of these constants.)