Efficient Integration: Substitution Method for 2x sec^2(x^2) dx

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    Integration
In summary, integration in science refers to the process of combining different pieces of information or ideas to create a comprehensive understanding of a topic or phenomenon. It is important in scientific research as it allows for a more holistic approach and promotes collaboration between different fields. Examples of integration in scientific studies include combining data from different experiments, integrating theories from multiple disciplines, and using various research methods. Integration contributes to the advancement of science by promoting a more accurate understanding of phenomena. However, some challenges of integration include the need for specialized knowledge in multiple fields, potential conflicts between theories or data sources, and the difficulty of finding a balance between different perspectives.
  • #1
rugapark
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the question is [tex]\int 2x sec^2 (x^2) dx[/tex]

do i sub u= sec (x^2) ?

I so far have got to trying to sub u= sec(x^2) and getting du= 2 (sec x^2 tan x^2)... i have a strong feeling i fudged the "du" part. hmm.
 
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  • #2
[tex]u=x^2[/tex]

[tex]du=2xdx[/tex] which you have! What is the anti-derivative of [tex]\sec^2 x[/tex] ?
 
  • #3
oh right, so I've got du=2xdx,

intergral sec^2 u du

= tan u + c

sub back u=x^2

=tan x^2 +c

how does that look?
 
  • #4
It looks just fine.
 

1. What is an integration in science?

An integration in science refers to the process of combining different pieces of information or ideas to create a comprehensive understanding of a topic or phenomenon. It involves using a variety of methods and data sources to form a cohesive and well-supported conclusion.

2. Why is integration important in scientific research?

Integration is important in scientific research because it allows scientists to take a multidisciplinary approach to studying complex topics. By integrating data from various fields and perspectives, scientists can gain a more thorough understanding of a subject and make more accurate conclusions.

3. What are some examples of integration in scientific studies?

Examples of integration in scientific studies may include combining data from different types of experiments, integrating theories from multiple disciplines, or using various research methods to address different aspects of a research question.

4. How does integration contribute to the advancement of science?

Integration contributes to the advancement of science by promoting a more holistic approach to understanding complex topics and by allowing for a more comprehensive and accurate understanding of phenomena. It also encourages collaboration and the exchange of ideas between different fields of study.

5. What are some challenges of integration in scientific research?

Some challenges of integration in scientific research include the need for specialized knowledge in multiple fields, potential conflicts between different theories or data sources, and the difficulty of finding a balance between different perspectives. It also requires a significant amount of time and effort to integrate data and ideas effectively.

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