Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2

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Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2

Integrate the following functions w.r.to ‘x’.
Question 1.
(i) (x + 5)6
(ii) \(\frac{1}{(2-3 x)^{4}}\)
(iii) \(\sqrt{3 x+2}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 1

Question 2.
(i) sin 3x
(ii) cos (5 – 11x)
(iii) cosec2 (5x – 7)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 2

Question 3.
(i) e3x – 6
(ii) e8 – 7x
(iii) \(\frac{1}{6-4 x}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 3

Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2

Question 4.
(i) sec2\(\frac{x}{5}\)
(ii) cosec (5x + 3) cot (5x + 3)
(iii) sec (2 – 15x) tan (2 – 15x)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 4
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 5

Question 5.
(i) \(\frac{1}{\sqrt{1-(4 x)^{2}}}\)
(ii) \(\frac{1}{\sqrt{1-81 x^{2}}}\)
(iii) \(\frac{1}{1+36 x^{2}}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 6

Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 Additional Problems

Question 1.
(3x + 4)6
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 7

Question 2.
\(\frac{1}{(x+5)^{4}}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 8

Question 3.
\(\frac{1}{p+q x}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 9

Question 4.
cos(4x + 5)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 10

Question 5.
cosec2(7 – 11x)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 11

Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2

Question 6.
sec(3 + x) tan(3 + x)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 12

Question 7.
cosec(3 – 2x) cot(3 – 2x)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 13

Question 8.
e3x + 2
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 14

Question 9.
\(\frac{1}{\sin ^{2}(l-m x)}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 15

Question 10.
(lx + m)1/2
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.2 16