Question

For what value of a is the area enclosed by r=theta, theta=0, and theta=a equal to 1?

Answer 1

@agent0smith do you how to do this?

Answer 2

using http://tutorial.math.lamar.edu/Classes/CalcII/PolarArea_files/eq0001MP.gif

since r=theta, plug that in, integrate....
\[\Large \int\limits_{0}^{a} \theta ^2 d \theta =1\]\[\Large \int\limits\limits_{0}^{a} \theta ^2 d \theta = \left[ \frac{ \theta^3 }{ 3 } \right]_{0}^{a} =1\]
plug in limits\[\Large \left[ \frac{ \theta^3 }{ 3 } \right]_{0}^{a} = \frac{ a^3 }{ 3 } - \frac{ 0^3 }{ 3 } = 1\]
\[\Large \frac{ a^3 }{ 3 } = 1\]so \[\Large a = \sqrt[3]{3}\]

Answer 3

@megannicole51 not 100% sure it's right...

Answer 4

it looks familiar let me look back at my notes! thank you soooo much:)

Answer 5

Welcome! Anytime :)