Integration Question (1 Viewer)

ALOZZZ

New Member
Joined
Aug 7, 2020
Messages
25
Gender
Female
HSC
2021
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

Well-Known Member
Joined
Dec 30, 2020
Messages
368
Gender
Male
HSC
2021
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

Joined
Jun 21, 2019
Messages
824
Location
Sydney
Gender
Male
HSC
N/A
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

Administrator
Administrator
Joined
Feb 16, 2005
Messages
8,113
Gender
Male
HSC
2006
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

Active Member
Joined
Aug 30, 2019
Messages
161
Location
Vern Gang
Gender
Male
HSC
2020
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

Member
Joined
Dec 15, 2017
Messages
122
Gender
Male
HSC
2019
Uni Grad
2024
I never know that HSC Advanced Maths has separable ordinary differential equations? lol
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top