Areas of Simple Closed Curves In Exercises 81-86, use a computer algebra system and the result of Exercise 77 to match the closed curse with its area. (These exercises were based on “The Surveyor's Area Formula'' by Bart Braden, College Mathematics Journal, September 1986. pp. 335-337, by permission of the author.) (a). 8 3 a b (b). 3 8 π a 2 (c). 2 π a 2 (d). π a b (e). 2 π a b (f). 6 π a 2 Deltoid: ( 0 ≤ t ≤ 2 π ) x = 2 a cos t + a cos 2 t y = 2 a sin t − a sin 2 t
Areas of Simple Closed Curves In Exercises 81-86, use a computer algebra system and the result of Exercise 77 to match the closed curse with its area. (These exercises were based on “The Surveyor's Area Formula'' by Bart Braden, College Mathematics Journal, September 1986. pp. 335-337, by permission of the author.) (a). 8 3 a b (b). 3 8 π a 2 (c). 2 π a 2 (d). π a b (e). 2 π a b (f). 6 π a 2 Deltoid: ( 0 ≤ t ≤ 2 π ) x = 2 a cos t + a cos 2 t y = 2 a sin t − a sin 2 t
Solution Summary: The author explains how to calculate the area of the curve in the interval ale x
Areas of Simple Closed Curves In Exercises 81-86, use a computer algebra system and the result of Exercise 77 to match the closed curse with its area. (These exercises were based on “The Surveyor's Area Formula'' by Bart Braden, College Mathematics Journal, September 1986. pp. 335-337, by permission of the author.)
(a).
8
3
a
b
(b).
3
8
π
a
2
(c).
2
π
a
2
(d).
π
a
b
(e).
2
π
a
b
(f).
6
π
a
2
Deltoid:
(
0
≤
t
≤
2
π
)
x
=
2
a
cos
t
+
a
cos
2
t
y
=
2
a
sin
t
−
a
sin
2
t
T
1
7. Fill in the blanks to write the calculus problem that would result in the following integral (do
not evaluate the interval). Draw a graph representing the problem.
So
π/2
2 2πxcosx dx
Find the volume of the solid obtained when the region under the curve
on the interval
is rotated about the
axis.
38,189
5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of the
solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x|
≤
and the curve y
y =
about the line
x =
=플
2
80
F3
a
FEB
9
2
7
0
MacBook Air
3
2
stv
DG
Find f(x) and g(x) such that h(x) = (fog)(x) and g(x) = 3 - 5x.
h(x) = (3 –5x)3 – 7(3 −5x)2 + 3(3 −5x) – 1
-
-
-
f(x) = ☐
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