Question

i need help with number 3 a and b

Answer 1

pls help

Answer 2

The opposite of derivative is integration, so in a you need to integrate once and on b, twice. Since the indefinite integral (with no limits of integration) gives you an arbitrary constant that disapears when you derivate, you need a way to find that constant because any number would satisfy the derivative formula since it would disapear when you derivated, thats why they give you one value of the function you want to find.
Is it too confusing the way I explained or you got it?

Answer 3

b was the confusing one,so am to integrate t-cosx 2twice?

Answer 4

Yes, because you are derivating twice, but then you get 2 arbitrary constants.

Answer 5

whats this for dy(0)/dx=2
what do i need it for?

Answer 6

my first integration i got tx-sin(x)+c

Answer 7

Your integration is fine and now you need to determine c, thats when you use dy(0)/dx=2, because by integrating once, you got dy/dx

Answer 8

so how do i use this dy(0)/dx=2?

Answer 9

tx-sin(x)+c=dy/dx
so
t*0-sin(0)+c=2
Do you understand that?

Answer 10

yeah

Answer 11

so what about the y(0)=-2?

Answer 12

you have dy/dx, but you want y, so you integrate again, and youll need this to find the other constant.

Answer 13

So, did you got the answer?

Answer 14

i will integrate this tx-sin(x)+c again?

Answer 15

yes

Answer 16

because it is equal to dy/dx, and you want y

Answer 17

i got (tx^2/2)+cos(x)+c

Answer 18

you forgot to sonsider the constant of the previous integration

Answer 19

There will be two constants in this case, because its the second derivative.

Answer 20

cx+tx^2/2+cos(x)+c?

Answer 21

Yep thats it, but keep in mind that the c's are different, and the first one you should already have it as a number

Answer 22

the 1st one is 2 right?

Answer 23

yes

Answer 24

ok thanks alot for your help :)

Answer 25

You are welcome