Question

1-Find the area of the region between the graphs of f and g, where f(x) = x^2-x-1 and g(x) = 5-X^2.

2-Arc Length. Find the length of the graph of f(x) = x^4 + 1/(32x^2) over the interval [1,2].

Answer #1

1. Find the area of the region bounded by the graph of the
function f(x) = x4 − 2x2 + 8, the
x-axis, and the lines x = a and
x = b, where a < b and
a and b are the x-coordinates of the
relative maximum point and a relative minimum point of f,
respectively.
2.Evaluate the definite integral.
26
2
2x + 1
dx
0
3. Find the area of the region under the graph of f...

Find the area of the region between the graphs of f(x) = 3x3 −
x2 − 10x and g(x) = −x2 + 2x.

Sketch the graphs of the functions.
f(x) = 3x
and g(x) = x squareoot
x+1
Find the area of the region completely enclosed by the graphs of
the given functions f and g.

Find the area completely enclosed by the graphs of f(x) = x^2 -
1 and g(x) = 1 - x^2

Find the area bounded between the graphs of f(x) = x3 + 11x2 −
11 and g(x) = 4x2 − 8x + 5. (A) 625/12 (B) 104/5 (C) 233/4 (D)
113/6 (E) 82/3

For the function f(x) = x, estimate the area of the region
between the graph and the horizontal axis over the interval 0≤x≤4
using a .
a. Riemann Left Sum with eight left rectangles.
b. Riemann Right Sum with eight right rectangles.
c. A good estimate of the area.

Estimate the area of the region bounded between the curve f(x) =
1 x+1 and the horizontal axis over the interval [1, 5] using a
right Riemann sum. Use n = 4 rectangles first, then repeat using n
= 8 rectangles. The exact area under the curve over [1, 5] is ln(3)
≈ 1.0986. Which of your estimates is closer to the true value?

A) Find an approximation of the area of the region R
under the graph of the function f on the interval [0, 2].
Use n = 5 subintervals. Choose the representative points
to be the midpoints of the subintervals.
f(x)=x^2+5
=_____ square units
B) Find an approximation of the area of the region R
under the graph of the function f on the interval [-1, 2].
Use n = 6 subintervals. Choose the representative points
to be the left endpoints...

f(x) = −x^2 + 5x and g(x) = 3x − 3 Find the area of the region
completely enclosed by the graphs of the given functions f and
g.

Find the area of the region bounded between the functions f(x)=
x2 – 2x + 2 and g(x) = -x2 + 6.

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