Integration Question (1 Viewer)

ALOZZZ

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Hey guys, there is a question about integration that I am having trouble with. It goes like this
A function has dy/dx= 4cos(2x) and passes through the point (pi/6, 2sqrt3). Find the exact equation of the function.
I know that y=2sin(2x) + C, but I don't know how to solve for C. Please help
 

Qeru

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Hey guys, there is a question about integration that I am having trouble with. It goes like this
A function has dy/dx= 4cos(2x) and passes through the point (pi/6, 2sqrt3). Find the exact equation of the function.
I know that y=2sin(2x) + C, but I don't know how to solve for C. Please help
Literally subsititute in the point so: and solve for C
 

Etho_x

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Hey guys, there is a question about integration that I am having trouble with. It goes like this
A function has dy/dx= 4cos(2x) and passes through the point (pi/6, 2sqrt3). Find the exact equation of the function.
I know that y=2sin(2x) + C, but I don't know how to solve for C. Please help
Soz writing with mouse a little messy
1610370670363.png
 

Trebla

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An alternative way using a definite integral rather than an indefinite integral that I have seen before.View attachment 29919
In the integrand, make sure you replace x/y with different variable names (e.g. u and v) to avoid confusing boundaries with variables.
 

vernburn

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In the integrand, make sure you replace x/y with different variable names (e.g. u and v) to avoid confusing boundaries with variables.
I agree 👍
The way I have presented it above is the way I was taught and the way I have always seen it presented. However, I was always cautious using it (and didn’t use it in my exams) because x/y are being treated both as variables and constants simultaneously which is dodgy to say the least!
 

Cujo10

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I never know that HSC Advanced Maths has separable ordinary differential equations? lol
 

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