Approximate the points at which the graphs of f ( x ) = 2 x 2 − 1 and g ( x ) = ( 1 + 4 x 2 ) − 3 / 2 intersect, and approximate the area between their graphs accurate to three decimal places.
Approximate the points at which the graphs of f ( x ) = 2 x 2 − 1 and g ( x ) = ( 1 + 4 x 2 ) − 3 / 2 intersect, and approximate the area between their graphs accurate to three decimal places.
Approximate the points at which the graphs of
f
(
x
)
=
2
x
2
−
1
and
g
(
x
)
=
(
1
+
4
x
2
)
−
3
/
2
intersect, and approximate the area between their graphs accurate to three decimal places.
a) Estimate the area under the graph of
f(x) = 7 + 4x2 from x = −1 to x = 2
using three rectangles and right endpoints.
R3 =
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 and the approximating rectangles for L6.
(c) Repeat part (a) using midpoints.
M3
=
M6
=
Sketch the curve and the approximating rectangles for M3.
Sketch the curve and the approximating rectangles for M6.
(d) From your sketches in parts (a)-(c), which appears to be the best estimate?
Find c> (such that the area of the region enclosed by
the parabolas y =
x² - c² and y = c²x² is
1944.
(a) The curves intersect when x is
. (Put the smaller one first.)
(b) The area of the region (as a function of C) is
(c) To get the area 1944, we take C =
and
Find the exact area between the graphs of f (x) = 2x +1 and g (x) = 9 – 22. First find out where the graphs intersect.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY