# Finding the value of integral.

• Raghav Gupta
In summary, the given integral is equal to π2/4 for n=1, but it is not necessarily true for all values of n. The rule mentioned is that ##\int_0^{2a} f(x)dx=2\int_0^a f(x)dx## if ##f(2a-x)=f(x)##.
Raghav Gupta

## Homework Statement

$$\int_0^{\pi} \frac{x(sinx)^{2n}}{(sinx)^{2n}+(cosx)^{2n}}$$ =
A) π2
B) 2π2
C) π2/4
D) π/2

## Homework Equations

$$\int_0^π f(x)dx = \int_0^π f(a-x)dx$$

## The Attempt at a Solution

If we put n = 1, we get the C option π2/4
But is it true for all n?

Remember that ##\int_0^{2a} f(x)dx=2\int_0^a f(x)dx## iff ##f(2a-x)=f(x)## and then consider the integral ##\int_0^{\pi} \frac{(sinx)^{2n}}{(sinx)^{2n}+(cosx)^{2n}}## using the rule you mentioned.

Raghav Gupta
certainly said:
Remember that ##\int_0^{2a} f(x)dx=2\int_0^a f(x)dx## iff ##f(2a-x)=f(x)## and then consider the integral ##\int_0^{\pi} \frac{(sinx)^{2n}}{(sinx)^{2n}+(cosx)^{2n}}## using the rule you mentioned.
Thanks, I got it certainly Calculus Cuthbert.

certainly
muffins from the cupboard ? no, no dear fellow I'm not hungry.

Raghav Gupta

## 1. How do I find the value of an integral?

Finding the value of an integral involves using mathematical techniques, such as integration by parts or substitution, to evaluate the integral. It is important to have a good understanding of calculus concepts and techniques in order to successfully find the value of an integral.

## 2. What is the purpose of finding the value of an integral?

The value of an integral is important in various fields of science, such as physics and engineering, as it can be used to calculate important quantities, such as area, volume, and displacement. It also allows us to solve differential equations and model real-life phenomena.

## 3. Can I use a calculator to find the value of an integral?

While calculators can be helpful in evaluating simple integrals, they are not always accurate and may not be able to solve more complex integrals. It is best to have a good understanding of calculus concepts and techniques to manually find the value of an integral.

## 4. Are there any specific steps to follow when finding the value of an integral?

Yes, there are various methods and techniques that can be used to find the value of an integral. Some common steps include identifying the function to be integrated, determining the limits of integration, and using appropriate integration techniques to evaluate the integral.

## 5. Is it possible to find the value of an integral without knowing the function?

No, it is not possible to find the value of an integral without knowing the function to be integrated. The function is a crucial component in the integral and without it, the value cannot be determined. However, in some cases, the function may not be explicitly given and may need to be derived from other information or equations.

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