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.
$$\frac{x}{\sqrt{1+x^{2}}}$$
Put 1 + x2 = u
2x dx = du
x dx = $$\frac{1}{2}$$ du

Question 2.
$$\frac{x^{2}}{1+x^{6}}$$

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

Question 3.
$$\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}$$

Question 4.

Question 5.

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

Question 7.

Question 8.

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.
$$\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}$$

Question 10.
$$\frac{\sqrt{x}}{1+\sqrt{x}}$$

Question 11.

Question 12.
α β xα-1 e-β xα
∫α β xα-1 e-β xα
Put β xα = u
α β xα-1 dx = du

Question 13.
$$\tan x \sqrt{\sec x}$$

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

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

Question 15.
sin5 x cos3 x
∫ 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.