a. 0.0788
b. 0.2736
c. 0.6024
d. 1.0472
e. 1.5590
f. 2.0708
g. 2.5156
h. 2.8444
i. 3.0392
j. 3.1180
or is it none of these ?
This is in polar coordinates, so you have to use the following formula:
A = 1/2∫r^2dΘ evaluated from alpha to beta
So, r = 2sinΘ, alpha =π/12 and beta = 3π/4, then replace:
A = ∫(2sinΘ)^2/2dΘ evaluated from π/12 to 3π/4
A = ∫4sin^2ΘdΘ evaluated from π/12 to 3π/4
Remember that:
sin^2Θ = (1 - cos(2Θ))/2
Then:
A = 2∫1 - cos(2Θ)dΘ
A = Θ - senΘ evaluated from π/12 to 3π/4
A = 3π/4 - sen(3π/4) - (π/12 - sen(π/12 ))
A = 1.646
Luix is correct
3.3460652
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Verified answer
This is in polar coordinates, so you have to use the following formula:
A = 1/2∫r^2dΘ evaluated from alpha to beta
So, r = 2sinΘ, alpha =π/12 and beta = 3π/4, then replace:
A = ∫(2sinΘ)^2/2dΘ evaluated from π/12 to 3π/4
A = ∫4sin^2ΘdΘ evaluated from π/12 to 3π/4
Remember that:
sin^2Θ = (1 - cos(2Θ))/2
Then:
A = 2∫1 - cos(2Θ)dΘ
A = Θ - senΘ evaluated from π/12 to 3π/4
A = 3π/4 - sen(3π/4) - (π/12 - sen(π/12 ))
A = 1.646
Luix is correct
3.3460652