
How to evaluate the definite integral of from to ?
Answer
442.8k+ views
Hint: To solve this question we need to know the concept of definite integral. We are given with the limits of the integral for the given function. For integrating the given function, the question will be solved using the method of integration by parts. So the formula used here will be , where and are the two functions.
Complete step by step answer:
To solve the integration of the function we should know the formula of the integration. The question is with limit as , which could be written as
The formula used to integrate the question is is , if the function is is and the function . Mathematically it will be written as:
On applying the formula we get , where on differentiating both side of the function we get:
Also the term is considered as , which means:
The above equation on integrating both side becomes:
Considering the formula the equation becomes:
On substituting the values on the above formula we get:
Integration of is .
On substituting the values on the function with the limits we get:
The value of and is not defined. Putting the values in the above expression, we get:
On further calculation it becomes:
The integration of the function from is .
Note: To solve this question we need to remember the formulas for integration, so that we do not make mistakes while writing the formulas. The above question has been solved by the method of integration by parts. The concept of definite integral is very useful and has a large number of applications. It is used to find the area of the enclosed figure etc.
Complete step by step answer:
To solve the integration of the function we should know the formula of the integration. The question is
The formula used to integrate the question
On applying the formula we get
Also the term
The above equation on integrating both side becomes:
Considering the formula the equation becomes:
On substituting the values on the above formula we get:
Integration of
On substituting the values on the function with the limits we get:
The value of
On further calculation it becomes:
Note: To solve this question we need to remember the formulas for integration, so that we do not make mistakes while writing the formulas. The above question has been solved by the method of integration by parts. The concept of definite integral is very useful and has a large number of applications. It is used to find the area of the enclosed figure etc.
Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
School Full course for MAHARASHTRABOARD students
₹33,300 per year
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
Why should a magnesium ribbon be cleaned before burning class 12 chemistry CBSE

A renewable exhaustible natural resources is A Coal class 12 biology CBSE

Megasporangium is equivalent to a Embryo sac b Fruit class 12 biology CBSE

What is Zeises salt and ferrocene Explain with str class 12 chemistry CBSE

Anal style is present in A Male cockroach B Female class 12 biology CBSE

A hollow metallic sphere of radius 10cm is given a class 12 physics CBSE
