Mathematics: Post your doubts here!

mmmmmm

mmmmmm

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Use the substitution u = sin 4x to find the exact value of cos^34x dx and the given range is (0 and 1/24pi)............Someone help me with this question.
 
ZaqZainab

ZaqZainab

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M Haseeb Javed said:
View attachment 40527

Part iii and iv please.
Click to expand...
Find the probability of R and S
R (4,4,3) (3,4,4) (4,3,4) <---all possible outcomes to get sum 11
P(R) ((6/10)*(5/9)*(4/8)) *3 =(1/2)
S (3,4,4,) (3,4,3) (3,3,3) (3,3,4)
P(S) ((4/10)*(6/9)*(5/8))+((4/10)*(6/9)*(3/8))+((4/10)*(3/9)*(2/8))+(4/10)*(3/9)*(2/8)) = 4/10
P(R and S)= (4/10)*(1/2)= 1/5
P (R intersection S) = Probability of (3,4,4)= 1/6
P(R and S) not equal to P (R intersection S) so not independent

Mutually exclusive means can't be both
It means when R takes place S can not but thats not true
P (R intersection S)= 1/6
so there is 1/6 probability that they both take place at the same time
P (R intersection S) not equal to 0
so Not Mutually Exclusive
 
sudeep1097

sudeep1097

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mmmmmm said:
Use the substitution u = sin 4x to find the exact value of cos^34x dx and the given range is (0 and 1/24pi)............Someone help me with this question.
Click to expand...

du/dx =4cos4x

and for integration of cos^3 4x write as cos4x * cos^2 4x dx
I am ignoring the integration sign now onwards.
=(4cos4x)/4 * (1-sin^2 4x) dx
=du/dx (1-sin^2 4x)/4 dx (the dx is cancelled here)
so (1-u^2)/4 du (since sin4x = u)
Now the new limits for integration are found using u=sin (1/24 pi) and u = sin (0)
you can take the 1/ 4 outside the integration sing to give 1/4[1-u^2 du] (i used brackets for integration sign)
now integrate with respect to du and solve to get the final answer since we have changed the limits you dont have to change u back to x.
 
mmmmmm

mmmmmm

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thanks, brother.

sudeep1097 said:
du/dx =4cos4x

and for integration of cos^3 4x write as cos4x * cos^2 4x dx
I am ignoring the integration sign now onwards.
=(4cos4x)/4 * (1-sin^2 4x) dx
=du/dx (1-sin^2 4x)/4 dx (the dx is cancelled here)
so (1-u^2)/4 du (since sin4x = u)
Now the new limits for integration are found using u=sin (1/24 pi) and u = sin (0)
you can take the 1/ 4 outside the integration sing to give 1/4[1-u^2 du] (i used brackets for integration sign)
now integrate with respect to du and solve to get the final answer since we have changed the limits you dont have to change u back to x.
Click to expand...
 
Talha Khatri

Talha Khatri

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Assalamualaikum guys, I had a doubt in this one, I was able to plot the argument and the mod correctly on the graph but I have no clue as to how do I get the last mod that's given in the question, any help please?
math.jpg
 
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