
Find the antiderivative of ?
Answer
476.1k+ views
Hint:Finding integral in just opposite of differentiation so for finding an integral you have to go reverse as in differentiation, it's quite easy when you get it. In this question you have to buy parts and you will have to use little bit of trigonometric identities as per requirement in the solution.
Formulae Used:
Complete step by step solution:
The given question is
After applying integration sign we get:
Here we are using the formulae of “cos(2x)” and integrating the term because direct integration of the given term is not available, hence we need to convert it into the given form, on solving we get:
Now we are using this conversion in our equation to solve the integral, and accordingly we will find the integral of the given term,
Here we get,
This is our required solution for the given equation.
Additional Information: You can check the answer by solving from bottom to top; just you have to differentiate the last equation until you get the fist equation. This method can take some time and several steps more than you take for integration but definitely you can get and verify.
Note: This is the easiest way to solve this question, but if you find any difficulty then you can try another method that is, use expansion of and after expansion you can integrate each term independently, then you can merge it and obtain your result. This method is appropriate for this kind of question.
Formulae Used:
Complete step by step solution:
The given question is
After applying integration sign we get:
Here we are using the formulae of “cos(2x)” and integrating the term because direct integration of the given term is not available, hence we need to convert it into the given form, on solving we get:
Now we are using this conversion in our equation to solve the integral, and accordingly we will find the integral of the given term,
Here we get,
This is our required solution for the given equation.
Additional Information: You can check the answer by solving from bottom to top; just you have to differentiate the last equation until you get the fist equation. This method can take some time and several steps more than you take for integration but definitely you can get and verify.
Note: This is the easiest way to solve this question, but if you find any difficulty then you can try another method that is, use expansion of
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
The non protein part of an enzyme is a A Prosthetic class 11 biology CBSE

Which of the following blood vessels in the circulatory class 11 biology CBSE

What is a zygomorphic flower Give example class 11 biology CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

The deoxygenated blood from the hind limbs of the frog class 11 biology CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
