What is the area under the polar curve #f(theta) = thetasin(-theta )+2cot((7theta)/8) # over #[pi/4,(5pi)/6]#?
Applying sum rule
Substituting
Rearranging
By signing up, you agree to our Terms of Service and Privacy Policy
To find the area under the polar curve ( f(\theta) = \theta \sin(-\theta) + 2\cot\left(\frac{7\theta}{8}\right) ) over the interval ( \left[\frac{\pi}{4}, \frac{5\pi}{6}\right] ), you can use the formula for finding the area under a polar curve:
[ A = \frac{1}{2} \int_{\alpha}^{\beta} [f(\theta)]^2 , d\theta ]
Where ( \alpha ) and ( \beta ) are the initial and final angles respectively.
Substitute the given function ( f(\theta) = \theta \sin(-\theta) + 2\cot\left(\frac{7\theta}{8}\right) ) into the formula, then integrate it with respect to ( \theta ) over the given interval ( \left[\frac{\pi}{4}, \frac{5\pi}{6}\right] ) to find the area under the curve.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
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 Cartesian form of #(36,(-pi)/16))#?
- How do you find the points of intersection of #r=4-5sintheta, r=3sintheta#?
- What is the distance between the following polar coordinates?: # (5,(19pi)/12), (3,(11pi)/8) #
- What is the Cartesian form of #(21,(pi )/2)#?
- What is the distance between the following polar coordinates?: # (2,(3pi)/8), (-8,(5pi)/8) #

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7