Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6

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Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6

Integrate the following with respect to x.
Question 1.
\(\frac{x}{\sqrt{1+x^{2}}}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 1

Question 2.
\(\frac{x^{2}}{1+x^{6}}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 2

Question 3.
\(\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 3

Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6

Question 4.
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 4
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 5
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 6

Question 5.
\(\frac{\sin \sqrt{x}}{\sqrt{x}}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 7

Question 6.
\(\frac{\cot x}{\log (\sin x)}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 8

Question 7.
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 9
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 10

Question 8.
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 11
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 12
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 13

Question 9.
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 14
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 15

Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6

Question 10.
\(\frac{\sqrt{x}}{1+\sqrt{x}}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 16
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 17

Question 11.
\(\frac{1}{x \log x \log (\log x)}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 18

Question 12.
αβxα-1e-βxα
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 19

Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6

Question 13.
\(\tan x \sqrt{\sec x}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 20
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 21

Question 14.
x(1 – x)17
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 22

Question 15.
sin5 x cos3 x
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 23

Question 16.
\(\frac{\cos x}{\cos (x-a)}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 24

Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 Additional Problems

Question 1.
(2x + 3)\(\sqrt{x^{2}+3 x-5}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 25

Question 2.
\(\frac{x \sin ^{-1}\left(x^{2}\right)}{\sqrt{1-x^{4}}}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 26

Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6

Question 3.
sec4 x tan x
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 27

Question 4.
\(\frac{\sin x}{\sin (x+a)}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 28

Question 5.
\(\frac{\sqrt{\tan x}}{\sin x \cos x}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 29
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 30

Question 6.
x(l – x)16
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 31

Question 7.
x2(2 – x)15
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 32

Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6

Question 8.
(x + 1)\(\sqrt{2 x+3}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 33
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 34

Question 9.
(x2)\(\sqrt{x+1}\)
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.6 35