write six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane xyz. evaluate the first integral.

Question

20-12-2022
Mathematics

Answered

write six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane xyz. evaluate the first integral.

Answer :

Other Questions

The file p08 23.xlsx contains data from a survey of 500 randomly selected households. a. separate the households in the sample by the location of their residenc

Taylor works on an art project that uses only rectangular pieces of paper. the first rectangle ha length 3/8 and width of 3in. detriment wether the dimensions o

1. when we cut the size of the training data set such that it contains the same number of rows with florence =1 as those with florence =0 , what is the impact o

the expression 1/2bh gives the area of a triangle where b is the base of the triangle and h is the height of the triangle

the measures of the angles of a 9-gon are in ratio $3:1:4:1:5:9:2:6:5.$ what is the number of degrees in the measure of the largest angle?

A randomly selected sample of marketing professionals was presented with various scenarios involving ethical issues. one issue was the use of ultraviolet ink on

The inner ring where measurements were taken has a 12-inch diameter. what was the volume of water [ft3] that infiltrated from this ring during the test

What is the slope of the line that passes through the points (-2,9) and (8,34)?

Translate the sentence into an equation. Twice the difference of a number and 9 is equal to 5. Use the variable w for the unknown number.

The dean of blotchville university boasts that the average class size there is 20. but the reality experienced by the majority of students there is quite differ

Anshuyadav Anshuyadav · Answer 1 · 2022-12-26T00:25:44-05:00

The iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane XYZ is 84

The term iterated triple integrals means the result of applying integrals to a function of more than one variable (for example or ) in a way that each of the integrals considers some of the variables as given constants.

Here we have to write six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane XYZ and then we have to evaluate the first integral.

Here in this case we will integrate with respect to y first.

Therefore, the iterated integral that we need to compute is,

∬6xy²dA=∫⁴₂∫₁²6xy²dydx

When we per the first stage integral, then we get,

=> ∫⁴₂ (2xy³)₁²dydx

When we expand it then we get,

=> ∫⁴₂ [16x - 2x] dx

=> ∫⁴₂ 14x dx

Then we further integrate this one, then we get.,

=> ∫⁴₂ 14x dx = [7x²]₂⁴

=> [7(4)² - 7(2)²]

=> 112 - 28

=> 84

To know more about Integration here.

https://brainly.com/question/18125359

#SPJ4