# Using advanced calculus for finding values

• MHB
• WMDhamnekar
In summary, the conversation is about finding positive integers A, B, C, D, and E for a given expression. The integral in the expression can be computed using numerical analysis. The solution to the question can be found on the Math Help Forum. The steps to solve the integral involve integration by parts and two substitutions.
WMDhamnekar
MHB
It is possible to find positive integers $A,B, C, D, E$ such that

$\displaystyle\int_0^{\frac{2a}{a^2+1}} sin^{-1}\big(\frac{|1-ax|}{\sqrt{1-x^2}}\big)dx=\frac{A}{\sqrt{a^2+1}}sin^{-1}\big(\frac{1}{a^B}\big ) - C sin^{-1} \big(\frac{1}{a^D}\big) + \frac {Ea\pi}{a^2+1}$ for all real numbers $a \geq 3$.

What is the value of A + B + C + D + E ?

How to answer this question?. The questioner also provided answer to this question. First he solved this question using integration by parts, then applying the substitution $(a^2+1)*x- a= a*sin\theta$. Then applying the substitution $t= tan \frac{\theta}{2}$

But I didn't understand some steps in his answer.

If any member of MHB knows the solution to this question, he may reply with correct answer.

Dhamnekar Winod said:
It is possible to find positive integers $A,B, C, D, E$ such that

$\displaystyle\int_0^{\frac{2a}{a^2+1}} sin^{-1}\big(\frac{|1-ax|}{\sqrt{1-x^2}}\big)dx=\frac{A}{\sqrt{a^2+1}}sin^{-1}\big(\frac{1}{a^B}\big ) - C sin^{-1} \big(\frac{1}{a^D}\big) + \frac {Ea\pi}{a^2+1}$ for all real numbers $a \geq 3$.

What is the value of A + B + C + D + E ?

How to answer this question?. The questioner also provided answer to this question. First he solved this question using integration by parts, then applying the substitution $(a^2+1)*x- a= a*sin\theta$. Then applying the substitution $t= tan \frac{\theta}{2}$

But I didn't understand some steps in his answer.

If any member of MHB knows the solution to this question, he may reply with correct answer.
This integral can be computed only with the help of numerical analysis. Classical calculus and trigonometry won't be of much help here.

Last edited:
Dhamnekar Winod said:
This integral can be computed only with the help of numerical analysis. Classical calculus and trigonometry won't be of much help here.

Any member of MHB curious about answer to this question can read it $\rightarrow$ http://mathhelpforum.com/calculus/283045-using-advanced-calculus-trigonometry-finding-values.html

Last edited:

## 1. What is advanced calculus?

Advanced calculus is a branch of mathematics that deals with the study of functions, limits, derivatives, and integrals of multiple variables. It is an extension of basic calculus and is used to solve complex problems in various fields such as physics, engineering, and economics.

## 2. How is advanced calculus used for finding values?

Advanced calculus is used to find values by using techniques such as optimization, integration, and differentiation. These methods allow us to analyze and manipulate complex functions to determine the maximum or minimum values, critical points, and inflection points.

## 3. Can advanced calculus be used in real-world applications?

Yes, advanced calculus is used in various real-world applications such as predicting stock market trends, optimizing production processes, and designing efficient structures. It is also used in fields like physics, where it is used to calculate the trajectory of objects and determine their optimal path.

## 4. What are the benefits of using advanced calculus over basic calculus?

The main benefit of using advanced calculus is its ability to solve more complex problems that cannot be solved using basic calculus. It also provides a deeper understanding of mathematical concepts and allows for more accurate and precise calculations.

## 5. Are there any resources available for learning advanced calculus?

Yes, there are many resources available for learning advanced calculus, including textbooks, online courses, and video lectures. It is recommended to have a strong foundation in basic calculus before delving into advanced calculus. Additionally, practicing and solving problems is essential for mastering advanced calculus.

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