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:

Question 2.
\(\frac{x^{2}}{1+x^{6}}\)
Solution:

Question 3.
\(\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}\)
Solution:

Question 4.

Solution:

Question 5.
\(\frac{\sin \sqrt{x}}{\sqrt{x}}\)
Solution:

Question 6.
\(\frac{\cot x}{\log (\sin x)}\)
Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.
\(\frac{\sqrt{x}}{1+\sqrt{x}}\)
Solution:

Question 11.
\(\frac{1}{x \log x \log (\log x)}\)
Solution:

Question 12.
αβx^α-1e^-βxα
Solution:

Question 13.
\(\tan x \sqrt{\sec x}\)
Solution:

Question 14.
x(1 – x)¹⁷
Solution:

Question 15.
sin⁵ x cos³ x
Solution:

Question 16.
\(\frac{\cos x}{\cos (x-a)}\)
Solution:

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:

Question 2.
\(\frac{x \sin ^{-1}\left(x^{2}\right)}{\sqrt{1-x^{4}}}\)
Solution:

Question 3.
sec4 x tan x
Solution:

Question 4.
\(\frac{\sin x}{\sin (x+a)}\)
Solution:

Question 5.
\(\frac{\sqrt{\tan x}}{\sin x \cos x}\)
Solution:

Question 6.
x(l – x)¹⁶
Solution:

Question 7.
x²(2 – x)¹⁵
Solution:

Question 8.
(x + 1)\(\sqrt{2 x+3}\)
Solution:

Question 9.
(x²)\(\sqrt{x+1}\)
Solution: