a level maths, rates of change, differentiation, year 2

a_level185

https://prnt.sc/ugnkun

question B please

Reply 1

davros

Original post by a_level185

https://prnt.sc/ugnkun

question B please

What have you tried so far?

What techniques do you know for solving 1st order DEs?

Reply 2

a_level185

Original post by davros

What have you tried so far?

What techniques do you know for solving 1st order DEs?

I’ve done all of part a. I haven’t studied A2 integration yet. This is part of a differentiation topic.

I know all of them. Chain rule, quotient rule, product rule. I know I have to integrate for part b though. But I don’t know how to separate the fraction . I did a^(3/2) * t^(-2) . But can I simply divide both sides by a^(3/2). Is there an invisible 1 on the left so I get 1/a^(-3/2) ?

Reply 3

mqb2766

Yes it's
Int A^(-3/2) dA = Int t^(-2) dt

Reply 4

a_level185

Original post by mqb2766

Yes it's
Int A^(-3/2) dA = Int t^(-2) dt

Ahh, I’m finding it hard to see how you got that.

I thought if you integrate using ln x rule then it’s a(3/2)ln (t^2) all divided by 2t

Reply 5

mqb2766

Original post by a_level185

Ahh, I’m finding it hard to see how you got that.

I thought if you integrate using ln x rule then it’s a(3/2)ln (t^2) all divided by 2t

Separation of variables. Divide both sides by A^(3/2) then integrate wrt t. The integral on the left becomes wrt dA as dA/dt dt becomes just dA.

Reply 6

a_level185

Original post by mqb2766

Separation of variables. Divide both sides by A^(3/2) then integrate wrt t. The integral on the left becomes wrt dA as dA/dt dt becomes just dA.

Ive just realised I’m confused because I am learning differentiation connected change of rates. Part b was off topic and differential equations (integration). So essentially I’m trying to attempt a question on something I’ve not yet learnt. I’ll learn it and have another go. Thanks for your help :smile: