Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 11 Integral Calculus Ex 11.6 Text Book Back Questions and Answers, Notes.

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

Question 1.
\(\frac{x}{\sqrt{1+x^{2}}}\)
Answer:
Put 1 + x2 = u
2x dx = du
x dx = \(\frac{1}{2}\) du
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 1

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

Question 2.
\(\frac{x^{2}}{1+x^{6}}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 2
Put x3 = u
3x2 dx = du
x2 dx = \(\frac{1}{3}\) du
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 3

Question 3.
\(\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 4

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

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

Question 5.
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 7
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 8

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

Question 6.
\(\frac{\cot x}{\log (\sin x)}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 9
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 10

Question 7.
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 11
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 12

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

Question 8.
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 13
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 14
Put a2 + b2 sin2x = u
(0 + b2 × 2 sin x cos x) dx = du
b2 sin 2x dx = du
sin 2x dx = \(\frac{1}{b^{2}}\) du
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 15

Question 9.
\(\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 16

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

Question 10.
\(\frac{\sqrt{x}}{1+\sqrt{x}}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 17
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 18
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 19

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

Question 11.
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 20
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 21

Question 12.
α β xα-1 e-β xα
Answer:
∫α β xα-1 e-β xα
Put β xα = u
α β xα-1 dx = du
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 22

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

Question 13.
\(\tan x \sqrt{\sec x}\)
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 23
put cos x = u
– sin x dx = du
sin x dx = – du
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 24
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 25

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

Question 14.
x (1 – x)17
Answer:
∫x (1 – x)17 dx
put 1 – x = u
-dx = du
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 26

Question 15.
sin5 x cos3 x
Answer:
∫ sin5 x cos3 x dx = ∫ sin5 x cos2 x . cos x dx
= ∫ sin5 x (1 – sin2 x) . cos x dx
= ∫ (sin5 x – sin7 x) . cos x dx
= ∫ sin5 x cos x dx – ∫ sin7 x cos x dx
put u = sin x
du = cos x dx
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 27

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

Question 16.
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 28
Answer:
Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.6 29

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