Answer
384.6k+ views
Hint: In this question, we have the trigonometric function which wants to integrate. To integrate the trigonometric function, we used a formula. And the formula is given below. First, we will convert that trigonometric function in the form of cosec function.
Complete step by step answer:
In this question, we use the word integration. First, we know about the integration. As we know Integration is defined as the process to find the function whose derivative is known. It is also called ant differentiation because the integration is the opposite process of differentiation. We know that differentiation is giving the rate of change of one variable with respect to another variable.
The main use of integration is to get back the function whose derivative is known.
If the function is \[f\left( x \right)\].then,
The integration form of that function is written as below.
\[ \Rightarrow \int_a^b {f\left( x \right)} dx\]
Here \[f\left( x \right)\] is a derivative whose upper limit is b and lower limit is a.
If
\[ \Rightarrow \dfrac{d}{{dx}}F\left( x \right) = f\left( x \right)\]
Then, we can write,
\[ \Rightarrow \int {f\left( x \right)} dx = F\left( x \right) + c\]
Here, \[F\left( x \right)\] is called the anti derivative function value of a given function\[f\left( x \right)\]. And \[c\] is known as the constant of integration and also called an arbitrary constant.
Now, come to the question. The data is given below.
\[ \Rightarrow \int {{{\cot }^2}xdx} \]
First, we convert \[\cot \]function in the form of \[\csc \]function as
\[ \Rightarrow \int {{{\cot }^2}} xdx = \int {\left( {\cos e{c^2}x - 1} \right)} dx\]
We will integrate each term separately,
\[ \Rightarrow \int {\cos e{c^2}} xdx - \int {dx} \]
Then, we integrate the above function as,
\[ \Rightarrow - {\cot }x - x + c\]
Therefore, the integration of \[\int {{{\cot }^2}xdx} \] is \[ - {\cot}x - x + c\].
Note:
As we know that if a function \[f\left( x \right)\], and integrate this function with respect to \[x\] is written as below.
\[\int {f\left( x \right)} dx\]
If \[\dfrac{d}{{dx}}f\left( x \right) = g\left( x \right)\]
Then we can write,
\[\int {g\left( x \right)} dx = f\left( x \right) + c\]
Here, \[c\]is called the constant of integration.
Complete step by step answer:
In this question, we use the word integration. First, we know about the integration. As we know Integration is defined as the process to find the function whose derivative is known. It is also called ant differentiation because the integration is the opposite process of differentiation. We know that differentiation is giving the rate of change of one variable with respect to another variable.
The main use of integration is to get back the function whose derivative is known.
If the function is \[f\left( x \right)\].then,
The integration form of that function is written as below.
\[ \Rightarrow \int_a^b {f\left( x \right)} dx\]
Here \[f\left( x \right)\] is a derivative whose upper limit is b and lower limit is a.
If
\[ \Rightarrow \dfrac{d}{{dx}}F\left( x \right) = f\left( x \right)\]
Then, we can write,
\[ \Rightarrow \int {f\left( x \right)} dx = F\left( x \right) + c\]
Here, \[F\left( x \right)\] is called the anti derivative function value of a given function\[f\left( x \right)\]. And \[c\] is known as the constant of integration and also called an arbitrary constant.
Now, come to the question. The data is given below.
\[ \Rightarrow \int {{{\cot }^2}xdx} \]
First, we convert \[\cot \]function in the form of \[\csc \]function as
\[ \Rightarrow \int {{{\cot }^2}} xdx = \int {\left( {\cos e{c^2}x - 1} \right)} dx\]
We will integrate each term separately,
\[ \Rightarrow \int {\cos e{c^2}} xdx - \int {dx} \]
Then, we integrate the above function as,
\[ \Rightarrow - {\cot }x - x + c\]
Therefore, the integration of \[\int {{{\cot }^2}xdx} \] is \[ - {\cot}x - x + c\].
Note:
As we know that if a function \[f\left( x \right)\], and integrate this function with respect to \[x\] is written as below.
\[\int {f\left( x \right)} dx\]
If \[\dfrac{d}{{dx}}f\left( x \right) = g\left( x \right)\]
Then we can write,
\[\int {g\left( x \right)} dx = f\left( x \right) + c\]
Here, \[c\]is called the constant of integration.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)