How Can You Solve This Challenging Integral Evaluation Problem?

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In summary, an integral evaluation problem involves using integration to find the area under a curve or the volume of a solid. It is solved by finding the antiderivative of a function and evaluating it at specific points. These types of problems have applications in various fields such as physics, engineering, and economics. The main challenges in solving them include finding the correct antiderivative and dealing with complex solutions. To improve skills in solving these problems, one can practice, use online resources, and seek help from a tutor. A strong understanding of calculus and algebra is also important.
  • #1
hadi amiri 4
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Evaluate
[tex]\int\frac{arctan(x)dx}{(1+x^2)^\frac{3}{2}}[/tex]
 
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Make the substitution:
[tex]x=\tan(u),\to\frac{dx}{du}=\frac{1}{\cos^{2}u}[/tex]
Thus, we get:
[tex]dx=\frac{du}{\cos^{2}(u)}[/tex]
and insertion in your integral yields:
[tex]\int\frac{arctan(x)}{(1+x^{2})^{\frac{3}{2}}}=\int{u}\cos(u)du[/tex]
 
  • #3


your solution seems nice
honestly i thought it is a hard one,becouse i picked it form "A coures of pure mathematics"
 

FAQ: How Can You Solve This Challenging Integral Evaluation Problem?

What is an integral evaluation problem?

An integral evaluation problem is a mathematical problem that involves finding the area under a curve or the volume of a solid using integration. It is essentially a way to calculate values that cannot be easily determined using basic algebra.

How is an integral evaluation problem solved?

An integral evaluation problem is solved using a process called integration, which involves finding the antiderivative of a function and evaluating it at specific points. This can be done using different techniques such as substitution, integration by parts, or using definite integrals.

What are the applications of integral evaluation problems?

Integral evaluation problems have various applications in fields such as physics, engineering, and economics. They are used to calculate areas, volumes, and other quantities that are important in these fields. For example, in physics, integrals are used to calculate work, energy, and center of mass.

What are the challenges of solving integral evaluation problems?

One of the main challenges of solving integral evaluation problems is finding the correct antiderivative of a function. This requires a good understanding of integration techniques and practice in solving different types of integrals. Additionally, some integrals may have complex solutions that require advanced mathematical knowledge to solve.

How can one improve their skills in solving integral evaluation problems?

To improve skills in solving integral evaluation problems, one can practice solving different types of integrals, use online resources and textbooks for guidance, and seek help from a tutor or teacher if needed. It is also important to have a strong foundation in calculus and algebra to better understand the concepts involved in solving integrals.

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