POST #30

AREA BETWEEN A CURVE:
FORMULA b(int)a (top eq.) - (bottom eq.): If a and b is not already given to you, then you much set the equations equal to each other and solve.Find which equation is top/bottom by graphing both and simply looking to see which one is on top.If the area is on the y-axis, then the a and b values need to be set as y-values, and the equations must be solved for x.

TANGENT LINE

1. find the x of your original function (usually given).
2. find the y of your original function (plug in x)
3. take derivative of original function.
4. plug x into derived function.
5. set up slope-intercept form.

NORMAL LINE

SAME FIST 4 STETPS..
STEP 5: make the slope perpendicular by flipping the fraction and making it negative.

PROMBLEM FROM AP: Compute the integral of 4x^2 (x^3+4) ^1/2 dx

u = x^3 +4 du= 3x^2

Get rid of the 3 in du, which you do by dividing something by 3 and gain a 4 which you do by multiplying by 4:

4/3 S u^1/2
4/3 (2/3 ) u ^3/2
8/9 ( x^3 +4) ^3/2 + c
ANSWER = C.

INTERMEDIATE VALUE THEOREM:
If f is continuous on [a,b] and k is any number between f(a)and f(b), then there is at least 1 number c when f(c)=k.


i don't understand the area under the curve problems on the AP test, my answer never comes out right.