1. Double Integral Applications 1a. Finding the Area of a Region Given the equations of two curves y = x² and y = 2x, perform the following tasks: i. Draw the region bounded by the given curves. ii. Use a double integral to find the area of the region. 1b. Finding the Surface Area of a Solid Given a paraboloid z = x² + y², find the surface area of the paraboloid in between z = 16 and z=4. 1c. Finding the Volume of a Solid Use double integral to determine the volume of z = √√4x² - y2 W

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For question 1B Draw paraboloid Z=x^2+y^2 

1. Double Integral Applications
1a. Finding the Area of a Region
Given the equations of two curves y = x² and y = 2x, perform the following tasks:
i. Draw the region bounded by the given curves.
ii. Use a double integral to find the area of the region.
1b. Finding the Surface Area of a Solid
Given a paraboloid z = x² + y², find the surface area of the paraboloid in between z = 16 and
z=4.
1c. Finding the Volume of a Solid
Use double integral to determine the volume of z = √√4x² - y2
W
Transcribed Image Text:1. Double Integral Applications 1a. Finding the Area of a Region Given the equations of two curves y = x² and y = 2x, perform the following tasks: i. Draw the region bounded by the given curves. ii. Use a double integral to find the area of the region. 1b. Finding the Surface Area of a Solid Given a paraboloid z = x² + y², find the surface area of the paraboloid in between z = 16 and z=4. 1c. Finding the Volume of a Solid Use double integral to determine the volume of z = √√4x² - y2 W
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