Find the exact length of the curve. y=ln(1-x^2), 0 ⩽x ⩽(1)/(2)

Name: Problem 17, Chapter 8: Calculus
Uploaded: 2020-05-30T15:14:48-08:00
Duration: 6 min 2 s
Channel: Rakesh Kumar Sharma
Description: Find the exact length of the curve. y=ln(1-x^2), 0 ⩽x ⩽(1)/(2)

step 1 Alright, so we have to find out the curve length for the curve which is given as y is equal to l

Find the exact length of the curve. y=ln(1-x^2), 0 ⩽x...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Arc Length Formula

The arc length formula is a fundamental concept in calculus which allows one to compute the length of a curve defined by a function over a given interval. It involves setting up an integral of the square root of 1 plus the square of the derivative of the function with respect to x, namely L = ?[a,b] ?(1 + (dy/dx)²) dx, which effectively sums infinitesimal segments along the curve.

Chain Rule in Differentiation

The chain rule is a key concept in differentiation that is used when finding the derivative of composite functions. It explains that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. This rule is critical in computing the derivative of the inside expression of functions like logarithms where an inner function is present.

Integration Techniques

Integration techniques are essential tools in calculus for evaluating integrals that do not readily yield to standard formulas. In problems involving the arc length formula, methods such as substitution or other algebraic manipulations are often employed to simplify the integrand, thereby facilitating the determination of an exact value for the length of the curve.

Transcript

Please give Ace some feedback