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 Cardiod: ( 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 Cardiod: ( 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 xl b.
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
Cardiod:
(
0
≤
t
≤
2
π
)
x
=
2
a
cos
t
−
a
cos
2
t
y
=
2
a
sin
t
−
a
sin
2
t
2. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.4.006.MI.
Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
7y2
y²
11
dy
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3. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.4.009.
Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
tan³(12/z) dz
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4. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.4.014.
Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)
5 sinб12x dx
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