How is the Area of a Polar Curve Derived from a Riemann Sum?

DoubleMike · 2005-02-17T02:01:13+00:00

Why is the area enclosed by a polar curve equal to \int \frac{1}{2}R^2 d\theta What's the Riemann sum from which this is derived?

Thread 'How does time derivative commute from one variable to another?'

I'm reviewing Meirovitch's "Methods of Analytical Dynamics," and I don't understand the commutation of the derivative from r to dr: $$ \mathbf{F} \cdot d\mathbf{r} = m \ddot{\mathbf{r}} \cdot d\mathbf{r} = m\mathbf{\dot{r}} \cdot d\mathbf{\dot{r}} $$

View full post »

Thread 'How does time derivative commute from one variable to another?'

Similar threads

Hot Threads

I Algebraic property of real numbers

I Problem in understanding instantaneous velocity

I How to find the path if we only know the velocity (without common formulas)?

I Harmonic series Ʃ1/n diverges but p-series Ʃ(1/n)^p diverges?

I Explicit logical justification for last step in epsilon/delta proof?

Recent Insights

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers

Insights Fermat's Last Theorem

Insights Why Vector Spaces Explain The World: A Historical Perspective