Question

Use the arc length formula to find the length of the curve y = 4x - 1, -3 lessthanorequalto x lessthanorequalto 2. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula. 4 Squareroot 17

Answer 1

Answer:

5$\sqrt{17}$ is the answer.

Step-by-step explanation:

y= 4x-1

taking derivative with respect to x ,we get $\frac{dy}{dx} = 4\\\\formula \int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^2 } } \, dx \\here a = 2 and b =-3 \\ \int\limits^2_{-3}_ {\sqrt{1+({4})^2 } } \, dx \\ = \sqrt{17} (2-(-3))=5\sqrt{17}$

Using distance formula

we have points

at x =-3 the value of y = 4(-3)-1= -12-1 = -13

at x =2 the value of y = 4(2)-1 =7

points are ( -3,-13) and (2,7)

distance formula =$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

                             =$\sqrt{(2-(-3)^2+(7-(-13)^2}$

                             =$\sqrt{(5)^2+(20)^2}$

                             =$\sqrt{425}$

                             =5$\sqrt{17}$