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

5
`√(17)` is the answer.

Explanation:

y= 4x-1

taking derivative with respect to x ,we get
`(dy)/(dx) = 4\\\\formula \int\limits^a_b {\sqrt{1+((dy)/(dx))^2 } } \, dx \\here a = 2 and b =-3 \\ \int\limits^2_(-3)_ {\sqrt{1+({4})^2 } } \, dx \\ = √(17) (2-(-3))=5√(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 =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

=
`√((2-(-3)^2+(7-(-13)^2)`

=
`√((5)^2+(20)^2)`

=
`√(425)`

=5
`√(17)`