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Engg. Maths - Calculus - Concept Card 3E

ENGG. MATHS - CALCULUS - CONCEPT CARD 3E

3E - PROPERTIES AND TECHNIQUES OF INTEGRATION

Properties of Definite Integrals:

i. Sums and Differences:

ii. Scalar Multiples:

 , c is any real number.

iii. Reversing the Limits:

iv. Concatenation:

 , p is a point inside [a,b].

Some Common Integrals:

a. 

b. 

c. 

d. 

e. 

f. 

g. 

h. 

i. 

j. 

k. 

l. 

m. 

n. 

Techniques of Integration:

i. Substitution Method:

Let, 

Then, 

ii. Integration by Parts:

It is best used to integrate a product when one factor  has a simple derivative and the other factor  is easy to integrate.

a. Indefinite Integrals:

i.e., 

b. Definite Integrals:

iii. Trigonometric Substitutions:

It is used to integrate expressions of the form 

a. Expression: 

Trig. Substitution
Expression becomes
Range of 
Identity used

b. Expression: 

Trig. Substitution
Expression becomes
Range of 
Identity used

c. Expression: 

Trig. Substitution
Expression becomes
Range of 
Identity used

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