Post #17

Calculus Week #17

Anyway so we are supposed to explain a concept and ask a question or two about another. Well to be quite honest, this week I actually learned something I should have known a long time ago.

Trapezoidal!

The formula is really simple and easy to remember...anyway, it's

Let x = (b-a)/n
x/2 [f(a) + 2f(a+x) + 2f(a+2x) ... f(b)]

This beats trying to find the actual area under the curve and wondering which one of the answer choices might be close. Lol...

Anyway, let's see...what else can I explain.

Okay a crash course to help you all on the take-home test:

If it asks for a tangent line, take the derivative, plug in x, get your slope, use that in point-slope form with the point you had with that slope.

If it asks for critical values...set derivative equal to 0 and solve for x.
Make sure to test end points.

Relative maximums or minimums are when you have multiple maxs and mins. The relative ones are the ones that are not absolute. The ones that are absolute are the ones that have either the highest y value or lowest y value.

Remember, if you are allowed in calculator, you can check your integration.

fnInt((equation),x,a,b) for f(x) = (equation) on the interval [a,b].

Or just plug it into y= on the plot then go to SECOND, CALC and go to the last option. Then type in a press ENTER then press b and press ENTER. Voila, a graphed picture of the area under your curve.

For the area between two curves, you do the top equation minus bottom equation. If you have no a,b to plug in, set the two equations equal and solve. Use that as your lower and upper bounds.

For volume by discs of a solid rotated about an axis, do the definite integral from a to b of the equation squared...times pi. Pretty simple.

For volume by washers, it's the same thing as area between two curves...except this time you square both equations as well, as in the above example.

Average value is 1/(b-a) times the definite integral from a to b of the function.

Average rate of change is a slope which is a derivative.

Derivative of position is velocity, derivative of velocity is acceleration.

So first derivative is velocity, second derivative is acceleration.

Let's see what else I can cover...

If they give you acceleration and you take the integral to find the velocity equation, don't forget you need to solve for +c. Usually they will give you some information such as v(1) = 1 would be used to plug in and solve for c.

Anyway, I think I gave a pretty decent crash course for the take home test. Don't forget to use your calculator...you can check almost all of the problems in your calculator so you might as well do it!