Calculating Arc Length for a Curved Function with a Starting Point of (0,1)

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In summary: i was getting confused because i was thinking it would be different than what the book said, but yeah that makes sense.
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ineedhelpnow
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find the arc length for the curve $y=sin^{-1}+\sqrt{1-x^2}$ with starting point (0,1).

$y'=\frac{1-x}{\sqrt{1-x^2}}$

$\int_{0}^{x} \ \sqrt{1+(\frac{1-x}{\sqrt{1-x^2}})^2},dx$

my answer is $\frac{-2\sqrt{2}*(\sqrt{\frac{1}{x+1}}-1)}{\sqrt{\frac{1}{x+1}}}$

i think my answer is wrong though
 
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I have moved your new question to a new thread. Please don't tag new questions onto existing threads. This makes threads harder to follow. :D
 
  • #3
ineedhelpnow said:
find the arc length for the curve $y=sin^{-1}+\sqrt{1-x^2}$ with starting point (0,1)...

What is the argument for the inverse sine function?

You go from an integral to a final answer...in order to more easily determine if you are correct and ensure you are doing things correctly, we need to see the intermediary steps. :D
 
  • #4
i only put it under the other thread because i didnt want to start too many new threads and they were the exact same topic. we're supposed to use our calculator for the question so i just put it in there. the answer in the back of the book is $2\sqrt{2}(\sqrt{1+x}-1)$
 
  • #5
ineedhelpnow said:
i only put it under the other thread because i didnt want to start too many new threads and they were the exact same topic. we're supposed to use our calculator for the question so i just put it in there. the answer in the back of the book is $2\sqrt{2}(\sqrt{1+x}-1)$

It is preferable to have more threads that deal with fewer problems per thread than fewer threads with many problems. The threads are easier to follow and allow for more efficient searching.

The answer you gave is equivalent to the more simplified answer given by your book. Take your answer and multiply by:

\(\displaystyle 1=\frac{\sqrt{1+x}}{\sqrt{1+x}}\)

and then distribute the negative sign out front into the factor in parentheses. :D
 
  • #6
oooh that makes sense.
 

FAQ: Calculating Arc Length for a Curved Function with a Starting Point of (0,1)

What is arc length?

Arc length is the distance along a curve or arc. It is the portion of the circumference of a circle or other curved figure.

How is arc length calculated?

Arc length can be calculated using the formula L = rθ, where L is the arc length, r is the radius of the circle or curve, and θ is the central angle in radians.

What is the significance of starting at (0,1) for arc length?

Starting at (0,1) is significant because it represents the starting point on the curve or arc. This point is often used as a reference point to calculate the arc length.

Can arc length be negative?

No, arc length cannot be negative. It is always a positive value representing the distance along the curve or arc.

How is arc length used in real-world applications?

Arc length is used in various fields such as engineering, physics, and mathematics to calculate the distance traveled along a curved path. It is also used in navigation systems, computer graphics, and robotics.

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