# What is the area under the polar curve #f(theta) = 3theta^2+thetasin(4theta-(5pi)/12 ) +cos(2theta-(pi)/3)# over #[pi/8,pi/6]#?

0.455

Doing this integral by hand would be little tedious so you can just plug integral in your calculator and get the answer.

The answer would be 0.455

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To find the area under the polar curve ( f(\theta) = 3\theta^2 + \theta\sin(4\theta - \frac{5\pi}{12}) + \cos(2\theta - \frac{\pi}{3}) ) over the interval ( \left[\frac{\pi}{8}, \frac{\pi}{6}\right] ), follow these steps:

- Compute the definite integral of ( f(\theta) ) over the given interval.
- Substitute the upper limit of integration into ( f(\theta) ) and subtract the result of substituting the lower limit of integration.
- Evaluate the resulting expression.

This will give you the area under the polar curve over the specified interval.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the distance between the following polar coordinates?: # (8,(5pi)/3), (1,(7pi)/4) #
- What is the distance between the following polar coordinates?: # (4,(-19pi)/12), (2,(-3pi)/8) #
- What is the distance between the following polar coordinates?: # (1,pi), (4,pi) #
- What is the slope of the tangent line of #r=theta-cos(4theta-(3pi)/4)# at #theta=(-2pi)/3#?
- What is the slope of the polar curve #f(theta) = sectheta - csctheta # at #theta = (3pi)/4#?

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