Arc Length of a Curve Using Parametric Equations

This video tutorial explains how to find the arc length of a curve given by parametric equations. It covers determining points on the curve for specific T values, applying the arc length formula, simplifying the integrand using algebra, and calculating the arc length with a decimal approximation. The tutorial provides a step-by-step approach, including the use of derivatives and integrals, to solve the problem effectively.

What is the starting point of the curve when T equals 0?

• (0, 1)

• (1, 1)

• (0, 0)

• (1, 0)

What is the y-coordinate of the curve when T equals PI over 2?

• 0

• 1

• PI

• e to the power of PI over 2

What is the significance of the point (0, e^(PI/2)) on the curve?

• It is the midpoint.

• It is the y-intercept.

• It is the endpoint.

• It is the x-intercept.

Which rule is used to find the derivatives of the parametric equations?

• Chain Rule

• Product Rule

• Quotient Rule

• Power Rule

What is the expression for dx/dt using the product rule?

• e^t * sin(t) - e^t * cos(t)

• -e^t * cos(t) + e^t * sin(t)

• e^t * cos(t) + e^t * sin(t)

• -e^t * sin(t) + e^t * cos(t)

What does the expression under the square root simplify to?

• e^(2t)

• 2e^(2t)

• 2e^t

• e^t

What does the expression 'sine squared T plus cosine squared T' simplify to?

• 1

• T

• 2

• 0

What is the integral of e^t with respect to t?

• e^(2t) + C

• 2e^t + C

• e^t + C

• e^(t^2) + C

What is the final expression for the arc length?

• sqrt(2) * (e^(PI/2) + 1)

• e^(PI/2) - 1

• 2 * (e^(PI/2) - 1)

• sqrt(2) * (e^(PI/2) - 1)

What is the approximate decimal value of the arc length?

• 4.888

• 5.388

• 6.388

• 5.888