- #1
haris13
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find the area of the double integral ∫∫x + y (is the triangular vertices (0.0) , (2,2) and (4,0)) how to find the values of x and y.
What have you tried? Before we can give you any help, you must have made an effort to solve the problem.haris13 said:find the area of the double integral ∫∫x + y (is the triangular vertices (0.0) , (2,2) and (4,0)) how to find the values of x and y.
What have you tried? Did you read my post #2?haris13 said:thanks for your help. I am fairly new at integrals so i was having a hard time. can you please give me the x and y values of both the intergrals of both parts. i still don't know how we arrive at those values. that's my only concern.
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A double integral is a type of calculus operation that involves finding the area under a 3-dimensional surface. It is essentially a combination of two single integrals, where the inner integral represents the integration over the x-axis and the outer integral represents the integration over the y-axis.
To find the area of triangular vertices using a double integral, you must first set up the integral using the formula "double integral of f(x,y) dA," where f(x,y) is the function representing the surface and dA represents the infinitesimal area element. Then, you must set the limits of integration to correspond with the vertices of the triangle. Finally, solve the integral to find the area.
The vertices of a triangle are important because they determine the limits of integration for the double integral. These limits represent the x and y values at which the surface intersects with the triangle, and thus, are crucial in accurately calculating the area.
Yes, a double integral can be used to find the area of any shape as long as the limits of integration are set correctly to correspond with the shape's boundaries. This includes not only triangular shapes, but also more complex shapes such as circles, ellipses, and irregular polygons.
Yes, there are many practical applications of using a double integral to find the area of triangular vertices. This concept is commonly used in fields such as engineering, physics, and economics to calculate the volume of objects, flow rates of fluids, and economic measures such as consumer surplus and producer surplus. It is also a fundamental concept in the study of multivariable calculus.