Chapter 1. calc_tutorial_15_4_021

1.1 Problem Statement

{2,4,5,7,8}
pow($a,2)
pow($a,3)
round(2*$c/3,3)

Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = $b, bounded above by the plane z = x and below by the xy-plane.

1.2 Step 1

Question Sequence

Question 1.1

Since one of the surfaces is a cylinder, it is best to use uW8Fu2zk58VicW40MbsbCyDoaq7NAmht0odJz0gMQGyksggYg+CPSczrE7Q= coordinates.

Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

The region D in the xy-plane is precisely the semicircle x2 + y2 = $b with x ≥ 0. Express D in polar coordinates.

0 ≤ r ≤ nc1ItEz0kR4=

-π / 2 ≤ θ ≤

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

Express the lower and upper bounds in polar coordinates.

lower bound z = 1Wh3cvJ2xF4=

upper bound z = x = 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

Correct.
Incorrect.

1.4 Step 3

Question Sequence

Question 1.3

Set up the triple integral for the volume in cylindrical coordinates.

xXq6LnspOhl4nbqqVo5oUfSECO0JmW39GWkxF2/l1Zu1MEYLy19JRsM3oFTisadGtXfR2lSaBQMB6ldUm1rEK4shJkYp39nY

Correct.
Incorrect.

1.5 Step 3

Question Sequence

Question 1.4

Evaluate the triple integral to find the volume of the given wedge-shaped region. Round your answer to three decimal places.

= U2GIbglD1oM=

Correct.
Incorrect.