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

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

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

Put x³ = u
3x² dx = du
x² dx = \(\frac{1}{3}\) du

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

Question 4.

Answer:

Question 5.

Answer:

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

Question 7.

Answer:

Question 8.

Answer:

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

Question 9.
\(\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}\)
Answer:

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

Question 11.

Answer:

Question 12.
α β x^α-1 e^{-β xα}
Answer:
∫α β x^α-1 e^{-β xα}
Put β x^α = u
α β x^α-1 dx = du

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

put cos x = u
– sin x dx = du
sin x dx = – du

Question 14.
x (1 – x)¹⁷
Answer:
∫x (1 – x)¹⁷ dx
put 1 – x = u
-dx = du

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

Question 16.

Answer: