Slope Of A Polar Curve

Length of Polar Curve Calculator + Online Solver With Gratuitous Steps

The Length of Polar Curve Calculator is an online tool to find the arc length of the polar curves in the Polar Coordinate organization.

A polar curve is a shape obtained by joining a ready of polar points with different distances and angles from the origin. This set of the polar points is defined past the polar role .

The result displays the verbal value of length and polar plot for the input function.

What Is a Length of Polar Curve Figurer?

A Length of Polar Curve Calculator is an online figurer that can be used to determine the arc length of polar function over a specified interval.

The arc length is a measure of altitude between two points forth a segment of the polar curve. This uncomplicated computer computes the arc length by quickly solving the standard integration formula defined for evaluating the arc length.

The formula for arc length of polar bend is shown beneath:

\[ Length = \int_{\theta=a}^{b} \sqrt{r^2 + (\dfrac{dr}{d\theta})^2} d\theta \]

Where the radius equation (r) is a function of the angle ($\theta$). The integral limits are the upper and lower limit of angle. The function is differentiated apropos the angle which is denoted past $dr/d\theta$.

Therefore, finding out the length needs several steps to be washed, which is a time-intensive procedure and there is a take chances of mistakes if solved by paw. But you can save your precious time by using this superb tool that provides you with the well-nigh authentic results.

This online calculator is readily available in your browser at whatever time and place. You don't need any prior noesis or require any skill to operate this calculator.

How To Use the Length of Polar Bend Estimator?

You tin can apply the Length of Polar Curve Calculator by inserting the values of the input components in their mentioned fields. Follow the given steps to go practiced results.

Step ane

Enter the polar equation which is a office of angle ($\theta$) in the Polar Equation R tab. Information technology can be whatsoever algebraic or trigonometric equation.

Footstep ii

Enter the starting bespeak of the angle in the box named From and the endpoint in the To box. The points can exist whatsoever value between 0 and $2\pi$.

Step iii

Printing the Submit button to become the desired event.

Result

The final result is provided in two steps. The commencement part is the length of the polar curve between the points you specified and the 2nd office is the polar graph that is fatigued inside that item bridge.

The polar graph displays the total polar curve in the dotted lines, whereas the specific portion of the curve for which arc length is evaluated is shown in a straight line .

Solved Examples

To farther clarify the use of the figurer, let'south explore some solved examples from this handy reckoner.

Example 1

Consider the following polar equation:

r($\theta$) = 6sin($\theta$)

The interval of angle for calculating the arc length is given equally:

\[ \theta = (0,\pi/2) \]

Solution

The calculator gives the following results.

Length of Polar Bend:

\[ \int_{0}^{\pi/ii} 6 d\theta = 3\pi \approx ix.4248 \]

Polar Plot:

The polar plot is depicted in Figure ane. The directly bold line represents the section of the curve for which arc length is calculated while the dotted line shows the remaining portion of the curve.

Effigy 1

Example 2

Consider the below-mentioned radius equation:

r($\theta$) = 5+cos(4$\theta$)

The integral limits for angle are as follows:

$\theta$ = (0,$\pi$)

Solution

For the above polar role, our calculator attains the following arc length and polar plot.

Length of Polar Curve:

\[ \int_{0}^{\pi} \sqrt{ (5+\cos(4\theta))^two + \sin^{2} (four\theta) } d\theta \approx 17.9971 \]

Polar Plot:

The polar plot is shown in Figure 2 beneath:

Figure 2

All the Mathematical Images/Graphs are created using GeoGebra.

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