area between curves
1. Find the area between x=1 and x=3 for: f(x) = x+4 and
g(x)=1
2. Find the area between x =-1 and x=1 for: f(x) = 2-x^2 and
g(x) =3
3. find the area between: f(x) = x^2 and g(x) = 2x+3
4. find the area between: f(x) = 4-x^2 and g(x) =3x
Approximate the area under f(x) = (x – 1)2, above the
x-axis, on [2,4] with n = 4 rectangles using the (a) left endpoint,
(b) right endpoint and (c) trapezoidal rule (i.e. the “average”
shortcut). Be sure to include endpoint values and write summation
notation for (a) and (b). Also, on (c), state whether the answer
over- or underestimates the exact area and why.
a) Find area between parabola f(x) = x^2/2p and its chord AB
which is perpendicular to y-axis. Here A(a,f(a)), B(-a, f(-a)),
a<0, p>0.
b) Show also that this area is 2/3 of the area of the rectangle
bounded by lines AB, X -axis, x = a,x = b.