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Math Assignment Class XII Ch -07 | Integrals
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Math Assignment Class XII Ch -07 | Integrals
MATHEMATICS ASSIGNMENT OF EXTRA QUESTION
Find the following integrals
Question 1
Answer: 4
Question 2
Answer
Question 3
Answer
Answer
Question 6
Answer: I = ex(1 - cot x) + C
Solution Hint
f(x) = 1 - cot x ⇒ f ' (x) = cosec2x
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
Evaluate:
Answer
Question 11
Evaluate:
Answer: π / 12
Solution Hint:
......(1)
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
Answer
Solution Hint
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
Question 17
Answer
Solution Hint:
Putting x2 = t then use partial fraction and then integrate
Question 19
Answer
Solution Hint
Separating the denominator we get
Question 20
Answer
Solution Hint
Taking x4 common from the numerator we get
............. (1)
I = I1 + I2
Putting tan x = t ⇒ sec2x dx = dt we get
Integrating this and putting the limit we get
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
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Comments
Keep going . Very good work.
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