How this calculation works
Find the exact-form arc length of a scaled parabola from the origin.
THE FORMULA
Integrate √(1+4a²x²) from 0 to the endpointA worked example
For a=1/2 and endpoint 1, the length is (√2+asinh 1)/2.
Good to know
The endpoint is nonnegative.
Reference: OpenStax Calculus Volume 3 (opens in a new tab) ↗
Read the result
Find the exact-form arc length of a scaled parabola from the origin.
The primary result is labeled “Arc length”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The endpoint is nonnegative.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
For a=1/2 and endpoint 1, the length is (√2+asinh 1)/2.
Which rule does this calculator apply?
Integrate √(1+4a²x²) from 0 to the endpoint