Estimate the area under the graph of f(x)=1/(x+4) over the
interval [-1,2] using five approximating rectangles and
right endpoints.
Rn=
Repeat the approximation using left endpoints.
Ln=
Estimate the area under the graph of f(x) =5 sqrt x. from x=0 to
x=4 using four approximating rectangles and right endpoints. sketch
the graph and rectangles. is your estimate an underestimate or
overestimate? Repeat using left endpoints
Approximate the area under the graph of f(x) and above the
x-axis with rectangles, using the following methods with
n=4.
f(x)=88x+55
from
x=44
to
x=66
a.
Use left endpoints.
b.
Use right endpoints.
c.
Average the answers in parts a and b.
d.
Use midpoints.
(a) Estimate the area under the graph of f(x) = 4 cos(x) from x
= 0 to x = π/2 using four approximating rectangles and right
endpoints. (Round your answers to four decimal places.) R4 = Sketch
the graph and the rectangles. WebAssign Plot WebAssign Plot
WebAssign Plot WebAssign Plot Is your estimate an underestimate or
an overestimate? underestimate overestimate (b) Repeat part (a)
using left endpoints. L4 = Sketch the graph and the rectangles.
WebAssign Plot WebAssign Plot WebAssign...
1) Find an estimate for the area under the graph of f(x)=x^2
from x=0 to x=8 using four rectangles and:
a) left end points
b) right end points
c) mid points
2) Find the volume of a solid obtained by rotating about the
x-axis the region bounded by y=x^3 and y=2x.
Sketch the region, the solid, and a typical disk or washer.
Estimate ∫^−3 −5 ?^2+5? ?? using midpoints for ?=4n=4 approximating rectangles.
∫^−3 −5 ?^2+5? ?? is approximately
Estimate ∫^3 2 2/? ?? using right endpoints for ?=3 approximating rectangles.
∫^3 2 2/? ?? is approximately
Consider the integral
∫102(4?^2+2?+6)??
(a) Find the approximation for this integral using left endpoints and ?=4
?4=
(b) Find the approximation for this same integral, using right endpoints and ?=4
?4=
(a) Estimate the area under the graph of
f(x) = 3 +
4x2 from x = −1 to
x = 2 using three rectangles and right
endpoints.
R3 =
Then improve your estimate by using six rectangles.
R6 =
Sketch the curve and the approximating rectangles for
R3 andR6.
(b) Repeat part (a) using left endpoints.
L3
=
L6
=
Sketch the curve and the approximating rectangles for
L3 and L6.
(c) Repeat part (a) using midpoints.
M3
=
M6...
(a) Estimate the area under the graph of
f(x) = 3 +
4x2 from x = −1 to
x = 2
using three rectangles and right endpoints.
R3 =
Then improve your estimate by using six rectangles.
R6 =
Sketch the curve and the approximating rectangles for
R3.
Sketch the curve and the approximating rectangles for
R6.
(b) Repeat part (a) using left endpoints.
L3
=
L6
=
Sketch the curve and the approximating rectangles for
L3.
Sketch the curve...
The graph of f(x) =2x + 1 is given below.
a. Use 4 approximating rectangles with right hand endpoints to
approximate the area under f(x) between x = 0 and x = 2.
b. Use a definite integral to find the exact area over the
interval [0. 2].