Mathematics: 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

Between the two answer is 3 hundred...

Use the arc length formula to find the length of

Ответ:

leslievramirez4074

13.03.2022

Mathematics

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 $\sqrt{17}$

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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

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