# Integration Question (1 Viewer)

#### ALOZZZ

##### New Member
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
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: $\bg_white 2\sqrt{3}=2sin\left(2 \times \frac{\pi}{6}\right)+C$ and solve for C

#### Etho_x

##### Well-Known Member
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

#### vernburn

##### Active Member
An alternative way using a definite integral rather than an indefinite integral that I have seen before.

#### ALOZZZ

##### New Member
Thank you guys soo much

#### Etho_x

##### Well-Known Member
Bro you wrote this with a mouse??? That's so damn neat...:O
Could be better but would probably need a tablet if I wanted to actually match up to my writing on paper lolz

#### Trebla

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