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Chapter 6: Q. 5TF (page 541)

Use this new description of arc length to show that the circumference of the unit circle is $2 π$ , by thinking of the unit circle as the parametric curve (cos $t, \sin t$ ) from $t = 0$ to $t = 2 π$ and applying the definite integral formula from the previous problem.

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Most popular questions from this chapter

Consider the region between the graph of $f (x) = x - 2$ and the x-axis on [2,5]. For each line of rotation given in Exercises 35– 40, use definite integrals to find the volume of the resulting solid.

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52

$\frac{d y}{d x} = 0.4 y - 100, y (0) = 0$

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52.

37. $\frac{d y}{d x} = x y, y (0) = - 1$

Find the exact value of the arc length of each function f(x) on [a, b] by writing the arc length as a definite integral and then solving that integral.

$f (x) = \sqrt{1 - x^{2}}$ , $[a, b] = [- 1, 1]$

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52

$\frac{d y}{d x} = e^{x + y}, y (0) = 2$

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Use this new description of arc length to show that the circumference of the unit circle is $2 π$ , by thinking of the unit circle as the parametric curve (cos $t, \sin t$ ) from $t = 0$ to $t = 2 π$ and applying the definite integral formula from the previous problem.

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Use this new description of arc length to show that the circumference of the unit circle is 2π, by thinking of the unit circle as the parametric curve (cos t,sint ) fromt=0 to t=2π and applying the definite integral formula from the previous problem.

Short Answer

Step by step solution

Step 1:

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Pure Maths

Calculus

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Use this new description of arc length to show that the circumference of the unit circle is $2 π$ , by thinking of the unit circle as the parametric curve (cos $t, \sin t$ ) from $t = 0$ to $t = 2 π$ and applying the definite integral formula from the previous problem.