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Math Assignment Class VIII | Square & Square Root

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  Math Assignment  Class VIII | Square & Square Root Download or Print free  assignment with answer key  for   Class  8 Squares and  Square Roots.   Important and extra questions that cover all topics of square and square root and is useful and helpful for the students. Math Assignment  Class VIII | Square & Square Root LEVEL -1

Math Assignment Class XII Ch -07 | Integrals

 Math Assignment  Class XII  Ch -07 | Integrals

Extra questions of chapter 07 Integrals class XII  with answers and  hints to the difficult questions, strictly according to the CBSE Board syllabus. Important and useful math. assignment for the students of class XII

MATHEMATICS ASSIGNMENT OF EXTRA QUESTION

STRICTLY ACCORDING TO THE PREVIOUS CBSE BOARD SAMPLE QUESTION PAPERS
FROM 2018 TO 2022

Find the following integrals

Question 1

Answer:  4

Question 2

Answer  

Question 3

Answer     

Question 4

Answer    

Question 5
 
Answer:  0
Solution Hint :  x2sinx is an odd function so this integral equal to zero

Question 6

Answer:  I = ex(1 - cot x) + C

Solution Hint

f(x) = 1 - cot x   ⇒  f ' (x) = cosec2

I = ex(1 - cot x)+C

Question 7

Answer    

Question 8

Answer    

Solution Hint

Now putting 1 - tan x = t

Question 9

Answer   

Solution Hint

Question 10

Evaluate:   

Answer     

Solution Hint
Taking '-' common from the denominator and then applying method of completing the square.

Question 11

Evaluate:  

Answer:  π / 12

Solution Hint:

   ......(1) 

 ..... (2)

Adding equation (1) and equation (2) we get

Question 12

Evaluate:  

Answer :  5

Solution Hint

x - 1 = 0 when x = 1, so given integral becomes

Integrate and putting the limit we get  I = 5

Question 13

Answer:  2

Question 14

Answer   

Solution Hint

 

 

Now integrating the first integral by parts we get




Question 15

 ...... (1)

Answer   

Solution Hint

Putting cos2x = t   ⇒  - 2 cosx sinx dx = dt  ⇒  Sin2x dx = - dt

Putting these values in equation (1) we get


Question 16

Answer    

Solution Hint:  Factorise the given function we get 


x(x - 1)(x - 2) = 0 ⇒ x = 0, 1, 2

Given integral can be written as 



Find the integrals and putting the limits we get


Question 17

Answer   

Solution Hint:

Putting x2 = t then use partial fraction  and then integrate

Question 18


Answer:  tan x - tan-1x + C

Solution Hint:

Adding and subtracting '1' in the numerator we get



Separating the denominator we get





I = tan x - tan-1x + C

Question 19

Answer   

Solution Hint

Separating the denominator we get

Question 20

Answer  

Solution Hint

Taking x4 common from the numerator we get

 ............. (1)

 

Differentiating both side we get


Putting all these values in eqn. (1) we get



Question 21
Answer: 2log2

Solution Hint

I = I1 + I2 

Since Iis an odd function so I1 = 0


Since is an even function so 




⇒ I = 2log2
Question 22

Answer   

Solution Hint:

Multiply and divide  by x we get


Now putting x2 = t   ⇒  2xdx = dt   ⇒ xdx = dt/2  we get


Using partial fraction to solve this integral


Solving these fractions we get,  A = 1, B = 0, C = - 2 and the given integral becomes






Question 23


Answer:   

Solution Hint



 





Question 24

Answer

Solution Hint



 

 


Putting sin x = t  ⇒ cosx dx = dt  we get


Now using partial fraction we get



Now putting  t = sinx we get


Question 25
 

Answer   

Solution Hint


  

 

⇒ f(x) = -f(x) ⇒ f(x) is an odd function so




⇒ g(-x) = g(x) ⇒ g(x) is an even function so


Now given integral becomes




 Divide  numerator and denominator by Cos2x we get



Putting  tan x = t   ⇒   sec2x dx = dt  we get

Integrating this and putting the limit we get

Question 26

Ans: 1
Solution Hint

 
 


Question 27


Ans:  

Question 28


Ans:  sin-1(sin x - cos x)

Solution Hint

Putting  sin x - cos x = t    (sin x + cos x)dx = dt

Squaring sin x - cos x = t on both side we get:  sin2x = 1- t2

Making all substitution we get




 

Question 29
Answer






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