how do i find the angle alpha and beta to form the integral? khan has not given any instructions
#Calculus: Area enclosed by polar curve
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pallid wagonBOT
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pallid wagonBOT
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rustic wing
wrong one anyway
rustic wing
how do i find the angle alpha and beta to form the integral? khan has not given ...
So notice at theta = 0 you have r = 1 and as theta slightly increases the radius becomes less until theta = 1/2 it would hit the origin since r = 0
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how would you know when theta = 1/2
rustic wing
now as you continue the second intersection is exactly on the negative y-axis
rustic wing
how would you know when theta = 1/2
1-2theta = 0?
bold yarrow
ohh i see what you mean
bold yarrow
now as you continue the second intersection is exactly on the negative y-axis
this is one of the main ones that I'm confused about. also the range given which is 0≤theta≤π
rustic wing
basically for the upper bound since it's on the y-axis what angle would correspond to the y-axis
you can use this relation too (-r, θ) = (r, θ+180°)
bold yarrow
π/2 or in this case 3π/2
bold yarrow
ohh so just use the one that would be in the range of 0≤theta≤π?
rustic wing
(-r,-π/2) = (r,π/2+π) = (r,π/2) actually
because radius is never negative we convert it to the actual angle
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i see
rustic wing
ohh so just use the one that would be in the range of 0≤theta≤π?
π/2 would correspond to the positive y-axis
but yes
leaden spearBOT
anti-algebraist 𝔸dωn𝓲²s
bold yarrow
okay yes this part i understand
alright thank you again
do you know how to put the solved mark
.close
pallid wagonBOT
Solved