(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...
Use finite approximation to estimate the area under the graph
f(x)= 8x2 and above graph f(x) = 0 from X0 =
0 to Xn = 16 using
i) lower sum with two rectangles of equal width
ii) lower sum with four rectangles of equal width
iii) upper sum with two rectangles of equal width
iv) upper sum with four rectangle of equal width
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 between the graph of f(x) = x3 − 12x and the
x-axis over the interval [−2, 1] using n = 6 rectangles and right
endpoints. Draw thecorresponding rectangles as well.
(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 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
Estimate the area A between the graph of the function f(x)=
square root of x and the interval [0,49]. Use an approximation
scheme with n=2,5, and 10 rectangles. Use the right
endpoints.
Round your answers to three decimal places.
A2=
A5=
A10=
Click