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### Math Assignment Class XII Ch -07 | Integrals

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# 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.**## 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

Find the following integrals

Question 1

**Answer: 4**

**Question 2**

**Answer **

**Question 3**

**Answer **

**Question 4**

**Answer **

**Question 5**

**Answer: 0**

**Solution Hint : x**

^{2}sinx is an odd function so this integral equal to zero**Question 6**

**Answer: I = e ^{x}(1 - cot x) + C**

**Solution Hint**

**f(x) = 1 - cot x ⇒ f ' (x) = cosec ^{2}x **

**I = e ^{x}(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: Ï€ / 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 cos ^{2}x = 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 x ^{2} = t then use partial fraction and then integrate**

**Question 18**

**Answer: tan x - tan**

^{-1}x + C**Solution Hint:**

**Adding and subtracting '1' in the numerator we get**

**Separating the denominator we get**

**I = tan x - tan**

^{-1}x + C**Question 19**

**Answer **

**Solution Hint**

**Separating the denominator we get**

**Question 20**

**Answer **

**Solution Hint**

**Taking x ^{4} 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 = I _{1} + I_{2} **

**Since I**

_{1 }is an odd function so I_{1}= 0

**Since is an even function so**

**⇒ I = 2log2**

**Question 22**

**Answer**

**Solution Hint:**

**Multiply and divide by x we get**

**Now putting x**

^{2}= 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 Cos**

^{2}x we get

**Putting tan x = t ⇒ sec ^{2}x 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- t ^{2}**

**Making all substitution we get**

**Question 29**

**Answer**

**Question 30**

**Solution :**

**Question 31**

**Find**

^{2}. then integrating w r t x we get

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### Comments

Keep going . Very good work.

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