Is there a best way to study calculus problems
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Is there a best way to study calculus problems

[From: ] [author: ] [Date: 11-08-15] [Hit: ]
dxi.e. a simple coef. can be taken outside integrandI(x^n) = (1/n)x^n+1I(sin ax) = - (1/a)cos (ax)I(cos ax)= (1/a)sin (ax)I(1/(x+a)) = log(x+a)Use substitutions you can need to practice a lot of these:e.g. ∫ 1/(x+1)² .......
d/dx ( f(g(x)) = g '(x) d/dg f(g)


for integration:

Indefinite integral is without limits,
I(x) = ∫ f(x).dx = F(x) +C where F(x) is the integral of f(x), C is arbitrary const.

Definite integral has limits and represents area (positive) under curve between the limits,
A = ∫ [a,b] f(x).dx = F(b) - F(a) this is called The foundamental theorem of calculus.
simply add areas identified where f(x) crosses the x-axis.

Some important integrals are:

∫ a.f(x).dx = a.∫f(x).dx i.e. a simple coef. can be taken outside integrand
I(x^n) = (1/n)x^n+1
I(sin ax) = - (1/a)cos (ax)
I(cos ax)= (1/a)sin (ax)
I(1/(x+a)) = log(x+a)

Use substitutions you can need to practice a lot of these:
e.g. ∫ 1/(x+1)² .dx subs: u = 1/(x+1) => - du = 1/(x+1)² .dx so
I(u) = ∫ -1 .du = - u +c ... notice carefully my notation
I(x) = -1/(x+1) +C

learn and practice your parts integration: ∫ u v'.dx = uv - ∫ u' v.dx - very important!

make sure you study some applied calculus v = ds/dt, a = v. dv/ds = dv/dt
and EOM (equation of motion) type problems,
e.g. the height of a particle h(t) = -16t^2 + vt +s etc. understand initial conditions
at t=0 height = 100 => h(0) = 100

I could go on and on but the above are the main areas where students of calculus get into difficulty.
get a decent book on calculus the ones used by undergraduates.

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If you want a nice book, I recommend Calculus with analytic geometry by Protter and Morrey.

Also, some sources:

khanacademy.org

http://www.youtube.com/user/UMKC#p/searc…

http://www.facebook.com/#!/pages/Calculu…

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Also, try to visualize the functions that you are integrating or taking the derivative of, and it helps to memorize some of the basic simple differentiation rules and integration rules.

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Do it over and over
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