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Polar integration

Just trying to get my head round how limits work on polar integration!
lol.png
(Drawing isnt great!)

But basically, if both the above were in polar form, so like the line is
r=π2r = \frac{\pi}{2}
and the curve was r=4cosθr = 4cos\theta
(randomly made up)
and the curve cut the axis at π\pi

To find the blue area, would the limits of
12\frac{1}{2} ∫π2π(4cosθ)2 dθ\displaystyle\int^\pi_\frac{\pi}{2} (4cos\theta)^2\ d\theta
give the blue area or blue and orange?
Original post by NiceToMeetYou
Just trying to get my head round how limits work on polar integration!
lol.png
(Drawing isnt great!)

But basically, if both the above were in polar form, so like the line is
r=π2r = \frac{\pi}{2}


More like θ=π4\theta=\frac{\pi}{4}


and the curve was r=4cosθr = 4cos\theta
(randomly made up)
and the curve cut the axis at π\pi


At π/2\pi/2 I think you mean


To find the blue area, would the limits of
12\frac{1}{2} ∫π2π(4cosθ)2 dθ\displaystyle\int^\pi_\frac{\pi}{2} (4cos\theta)^2\ d\theta
give the blue area or blue and orange?


12\frac{1}{2} ∫π4π2(4cosθ)2 dθ\displaystyle\int^\frac{\pi}{2}_{\frac{\pi}{4}}(4cos\theta)^2\ d\theta

gives the area in blue.
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NiceToMeetYou
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Original post by ghostwalker
More like θ=π4\theta=\frac{\pi}{4}



At π/2\pi/2 I think you mean



12\frac{1}{2} ∫π4π2(4cosθ)2 dθ\displaystyle\int^\frac{\pi}{2}_{\frac{\pi}{4}}(4cos\theta)^2\ d\theta

gives the area in blue.


Is there an explanation as to why, obviously with cartesian coordinates integrating between the axis and intersect would give blue and orange

Posted from TSR Mobile
Original post by NiceToMeetYou
Is there an explanation as to why, obviously with cartesian coordinates integrating between the axis and intersect would give blue and orange

Posted from TSR Mobile


It should be in your textbook.

The intgral gives the area defined by the two values of theta and from the origin to the curve.

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