OK explanations for my 3rd academic detention.
Integration
riemann summs...
Lram-left hand approximation
deltax[f(a)+f(a+deltax)+.....f(b+deltax)]
Rram-right hand approximation
deltax[f(a+delta x)+....f(b)]
Mram
deltax[f(mid)+f(mid)+....]
trapezoid
deltax/2[f(a)+2f(a+deltax)+2f(a+2deltax).....f(b)]
Another integration process is washers and disk
Disk are used with solid objects and the formula is
=(pie) b/s/a[R(x)]^2dx
and washers are for objects with holes and the formula is
=(pie)b/s/a top^2-bottom^2 dx
Ex Find the volume of the solid formed by revolving the region bounded by the graphs of y=squareroot of x and y=x^2
after graphing in your graphing calculater you find that you need to use washers
so you get =(pie)S(squareroot of x)^2-(x^2)^2 dx
x=1 so (pie)[(1/2)-(1/5)]-0
3(pie)/10 is your awnser
and for another big problem i have in calulus is optamization
Subscribe to:
Post Comments (Atom)
For optimization you will always have two equasions: a primary and a secondary. The primary will always be the one you're asked to minimize or maximize. The secondary will always be set equal to a number.
ReplyDeleteSteps:
1. Find primary and secondary equations
2. Solve secondary for one variable
3. Plug into primary
4. Take derivative
5. Set equal to zero and solve
6. Plug value back into secondary, solve for the remainding variable
*Usually in optimization problems, they'll ask for two answers. Steps 5 and 6 will give you these answers.