Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) PDF Download

Double Integrals

The double integral of a function f(x, y) over a region D is denoted by Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) . Let f(x, y) be a continuous function defined on a closed rectangleDouble and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

For continuous functions f(x, y) we haveDouble and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

Solved Numericals (Double Integrals)

Q1. Evaluate Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE).

Solution: 
Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)


Q2. Evaluate Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE).
Solution: 

Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

Triple Integrals

A triple integral of a function defined over a region R is denoted by
Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

Evaluation of Triple Integrals :
If the region R can be described by
Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

then we evaluate triple integral asDouble and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

Note: There are six possible ways in which a triple integral can be evaluated (order of variables of integration). We choose the one which is simple to use 

Solved Numericals (Triple Integrals)

Q1. Evaluate Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE).
Solution: 
Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
…(Integrating w.r.t. z keeping x, y constants)
Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

…(integrating w.r.t. y keeping x constant)
Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)



Q2. Evaluate Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE).
Solution:
Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)


Q3. Evaluate Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE).
Solution:
Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

The document Double and Triple Integrals | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Engineering Mathematics for Electrical Engineering.
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FAQs on Double and Triple Integrals - Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

1. What is the difference between double integrals and triple integrals in mechanical engineering?
Ans. In mechanical engineering, double integrals involve integrating a function over a two-dimensional region, while triple integrals involve integrating a function over a three-dimensional region.
2. How are double integrals used in mechanical engineering applications?
Ans. Double integrals are commonly used in mechanical engineering to calculate properties such as area, volume, mass, and moments of inertia for various components and structures.
3. What are some common challenges faced when solving double and triple integrals in mechanical engineering problems?
Ans. Some common challenges include determining the limits of integration, handling complex geometry, and correctly setting up the integrals to represent the physical quantities of interest.
4. Can you provide an example of a practical application where triple integrals are used in mechanical engineering?
Ans. One practical application of triple integrals in mechanical engineering is determining the center of mass for a three-dimensional object with non-uniform density distribution.
5. How can engineers optimize the use of double and triple integrals in mechanical design processes?
Ans. Engineers can optimize the use of integrals by breaking down complex shapes into simpler geometric components, utilizing software tools for numerical integration, and understanding the physical significance of the results obtained from the integrals.
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