7. Section 8.1 Length of a Curve

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7. Section 8.1 Length of a Curve Table of Contents 7. Section 8.1 Length of a Curve

Length of a Curve Essential Question How do you find the length of a curve using integrals and derivatives?

Length of a curve

Length of a curve

Length of a curve

Formula Derivation

Formula derivation continued….

Length of a Curve

Example Find the length of y = sin x from x = 0 to x =

Example Find the length of from x = 0 to 1

Example – Vertical Tangent Find the length of from (-8,-2) to (8,2) Can’t take derivative because of vertical tangent at y = 0 so change to function of y

Example – Cusp or Corner Find the length of from x = -4 to x = 4 Can’t take derivative because of corner so split into two parts

Example Show using calculus that the circumference of a circle with radius 5 is 10

Assignment Pg. 485 #1-9 odd, 15, 17, 23