i need help with number 3 a and b

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i need help with number 3 a and b

Mathematics
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pls help
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?

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b was the confusing one,so am to integrate t-cosx 2twice?
Yes, because you are derivating twice, but then you get 2 arbitrary constants.
whats this for dy(0)/dx=2 what do i need it for?
my first integration i got tx-sin(x)+c
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
so how do i use this dy(0)/dx=2?
tx-sin(x)+c=dy/dx so t*0-sin(0)+c=2 Do you understand that?
yeah
so what about the y(0)=-2?
you have dy/dx, but you want y, so you integrate again, and youll need this to find the other constant.
So, did you got the answer?
i will integrate this tx-sin(x)+c again?
yes
because it is equal to dy/dx, and you want y
i got (tx^2/2)+cos(x)+c
you forgot to sonsider the constant of the previous integration
There will be two constants in this case, because its the second derivative.
cx+tx^2/2+cos(x)+c?
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
the 1st one is 2 right?
yes
ok thanks alot for your help :)
You are welcome

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