Explanation Given: r ( t ) = ( cos t , tan t , t ) , 0 ≤ t ≤ π 4 Formula used: d d t t n = n t n − 1 ∫ t n d t = t n + 1 n + 1 d cos t d t = − sin t , d tan t d t = − sec 2 t , ∫ tan t d t = ln | sec t | ∫ u v d x = u ∫ v d x − ∫ d u d x ∫ v d x d x Calculation: x = cos t , y = tan t , z = t d x = − sin t d t d y = sec 2 t d t d z = d t ∫ c z d x + x 2 d y + y d z = − ∫ 0 π / 4 t sin t d t + ∫ 0 π / 4 cos 2 t ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.2, Problem 32E

To determine

To evaluate: The line integral $\int_{c} z d x + x^{2} d y + y d z$ where C is $r (t) = (\cos t, \tan t, t), 0 \leq t \leq \frac{π}{4}$

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Chapter 17.2, Problem 31E

Chapter 17.2, Problem 33E

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Chapter 17 Solutions

CALCULUS (CLOTH)

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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The line integral ∫ c z d x + x 2 d y + y d z where C is r ( t ) = ( cos t , tan t , t ) , 0 ≤ t ≤ π 4

Solution Summary: The author explains how the line integral c z d x + y = r (t) = cos t, n.

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To evaluate: The line integral $\int_{c} z d x + x^{2} d y + y d z$ where C is $r (t) = (\cos t, \tan t, t), 0 \leq t \leq \frac{π}{4}$

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Chapter 17 Solutions

The line integral ∫ c z d x + x 2 d y + y d z where C is r ( t ) = ( cos t , tan t , t ) , 0 ≤ t ≤ π 4

Solution Summary: The author explains how the line integral c z d x + y = r (t) = cos t, n.

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To evaluate: The line integral ∫czdx+x2dy+ydz where C is r(t)=(cost,tant,t),0≤t≤π4

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Chapter 17 Solutions

To evaluate: The line integral $\int_{c} z d x + x^{2} d y + y d z$ where C is $r (t) = (\cos t, \tan t, t), 0 \leq t \leq \frac{π}{4}$