Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 11 Integral Calculus Ex 11.1 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.1

Integrate the following with respect to x:

Question 1.
(i) x11
(ii) $$\frac{1}{x^{7}}$$
(iii) $$\sqrt[3]{x^{4}}$$
(iv) (x5)1/8
(i) x11

(ii) $$\frac{1}{x^{7}}$$

(iii) $$\sqrt[3]{x^{4}}$$

(iv) (x5)1/8

Question 2.
(i) $$\frac{1}{\sin ^{2} x}$$
(ii) $$\frac{\tan x}{\cos x}$$
(iii) $$\frac{\cos x}{\sin ^{2} x}$$
(iv) $$\frac{1}{\cos ^{2} x}$$
(i) $$\frac{1}{\sin ^{2} x}$$
$$\frac{1}{\sin ^{2} x}$$ = ∫cosec2 x dx
= – cot x + c

(ii) $$\frac{\tan x}{\cos x}$$
$$\frac{\tan x}{\cos x}$$ = ∫sec x tan x dx
= sec x + c

(iii) $$\frac{\cos x}{\sin ^{2} x}$$

(iv) $$\frac{1}{\cos ^{2} x}$$
$$\frac{1}{\cos ^{2} x}$$ = ∫sec2 x dx
= tan x + c

Question 3.
(i) 123
(ii) $$\frac{x^{24}}{x^{25}}$$
(iii) ex
(i) 123
∫123 dx = 123 ∫dx = 123x + c

(ii) $$\frac{x^{24}}{x^{25}}$$

(iii) ex
∫ex dx = ex + c

Question 4.
(i) (1 + x2)-1
(ii) (1 – x2)-1/2