How to remember integrals of some particular functions?

7 Views|Posted 5 months ago
Asked by Shiksha User
1 Answer

Below are a few important tips to remember the integrals of some particular functions:
1. Know the derivatives for each integral.
2. Make yourself familiar with the standard formulas first.
3. Practice daily for better memory.
4. Group similar formulas

Thumbs Up IconUpvote Thumbs Down Icon

Similar Questions for you

I = 0 π / 4 x d x s i n 4 ( 2 x ) + c o s 4 ( 2 x )

           Let 2x = t then   d x = 1 2 d t

I = t 2 1 2 d t s i n 4 t + c o s 4 t

= 1 4 0 π / 2 t d t s i n 4 t + c o s 4 t d t            

I = 1 4 0 π / 2 ( π 2 t ) d t s i n 4 t + c o s 4 t d t

2 I = 1 4 0 π / 2 π 2 d t s i n 4 t + c o s 4 t

2 I = 1 4 0 π / 2 π 2 d t s i n 4 t + c o s 4 t

2 I = π 8 0 π / 2 s i n 4 t d t t a n 4 t + 1            

Let tan t = y then

2 I = π 8 0 ( 1 + y 2 ) d y 1 + y 4             

= π 8 0 1 + 1 y 2 y 2 + 1 y 2 2 + 2 d y

= π 8 0 ( 1 + 1 y 2 ) d y 2 + ( y 1 y ) 2             

Let

...Read more

k = [ a b c ] + 2 [ a b c ] + [ a b c ] [ a b c ] [ a b c ]            

k = 3

...Read more

l i m x 0 [ s i n 2 ( π 2 3 x ) ] s e c 2 ( π 2 5 x )

e l i m x 0 [ s i n 2 ( π 2 3 x ) 1 ] s e c 2 ( π 2 5 x )

= e l i m x 0 s i n 2 ( 3 π x 2 ( 2 3 x ) ) s i n 2 ( 5 π x 2 ( 2 5 x ) ) = e 9 2 5

The integral is I = ∫ [ (x²-1) + tan? ¹ (x + 1/x)] / [ (x? +3x²+1)tan? ¹ (x+1/x)] dx
This is a complex integral. The provided solution splits it into two parts:
I? = ∫ (x²-1) / [ (x? +3x²+1)tan? ¹ (x+1/x)] dx
I? = ∫ 1 / (x? +3x²+1) dx
The solution proceeds with substitutions which are hard to follow due

...Read more

The problem is to evaluate the integral:
I = ∫? ¹? [x] * e^ [x] / e^ (x-1) dx, where [x] denotes the greatest integer function.

The solution breaks the integral into a sum of integrals over unit intervals:
I = ∑? ∫? ¹ n * e? / e^ (x-1) dx
= ∑? n * e? ∫? ¹ e^ (1-x) dx
= ∑? n * e? [-e^ (1-x)] from n to n+1

...Read more

Taking an Exam? Selecting a College?

Get authentic answers from experts, students and alumni that you won't find anywhere else.

On Shiksha, get access to

66K
Colleges
|
1.2K
Exams
|
6.9L
Reviews
|
1.8M
Answers

Learn more about...

NCERT Notes 2025

NCERT Notes 2025

View Exam Details

Most viewed information

SummaryNews

Share Your College Life Experience

Didn't find the answer you were looking for?

Search from Shiksha's 1 lakh+ Topics

or

Ask Current Students, Alumni & our Experts

Have a question related to your career & education?

or

See what others like you are asking & answering