Maths Advanced Integration Questions (1 Viewer)

[Farhanthestudent005]

I would appreciate if someone could send me the solutions to these so I can understand them. I have been struggling with them for quite a while.

 

[ExtremelyBoredUser]

View attachment 34914View attachment 34915
I would appreciate if someone could send me the solutions to these so I can understand them. I have been struggling with them for quite a while.

Any question in particular or all of them?

You can treat derivatives as fractions so you can rearrange them so you get one side with dx and other side with dt and integrate it, then you can find the constant term by substituting initial values. Remember that angle of inclination relates to the gradient from m = tan(x) so you can find the gradient from the angle it makes.

These questions are just using prelim adv concepts in integration so if you're struggling with getting the links between the information they give you and what to do then it might help revising coordinate geometry from year 11 adv.

 

[jimmysmith560]

Would the following working help with question 18?



Integrating, we get:



In order to find the value of this constant, we need to understand that the gradient of the tangent at (-1,3) is perpendicular to the gradient of the line

Rearranging results in:

Therefore, the gradient of the tangent is 2, as the product of perpendicular gradients is -1.

Substituting this into :



Integrating again, we get:


The point (-1,3) is on this curve. Using this information in the equation:



Hence, the equation of the curve is:

 

[jiminycricket123]

 

[jiminycricket123]

 

[jiminycricket123]

Hope that helps!

 

[lmao1010]

Hope that helps!

What book is that btw?

 

[5uckerberg]

What book is that btw?

The laughing stock in the Bored of Studies community for students who do maths.
Also, the book that people try to steer you away from and go into Cambridge and past papers written by Margaret Grove.

 

[jiminycricket123]

What book is that btw?

Maths in Focus

 

[lmao1010]

Maths in Focus

Ah k