Question 1: (x – 2)2 √x

Step-by-step solution provided.

Question 7: cos 3x cos 2x cos x

Step-by-step solution provided.

Maharashtra State Board Class 12 (HSC Board) Mathematics & Statistics Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 - Digest Answers | Maharashtra Board Solutions

Balbharti12th Maharashtra State Board Maths Solutions BookPdf Chapter 3 Indefinite Integration Miscellaneous Exercise 3 Questions and Answers.

Maharashtra State Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3

I. Choose the correct options from the given alternatives:

Question 1 Maharashtra Board Solution

(a) (b) (c) (d)

Solution & Step-by-Step Answer:

(b)

Question 2 Maharashtra Board Solution

= f(x) + c, then (a) log x – f(x) + c (b) f(x) + log x + c (c) f(x) – log x + c (d) x5 f(x) + c

Solution & Step-by-Step Answer:

(a) log x – f(x) + c

Question 3 Maharashtra Board Solution

(a) log(3x) – log(9x) + c (b) log(x) – (log 3). log(log 9x) + c (c) log 9 – (log x). log(log 3x) + c (d) log(x) + log(3). log(log 9x) + c

Solution & Step-by-Step Answer:

(b) log(x) – (log 3). log(log 9x) + c

Question 4 Maharashtra Board Solution

(a) (b) (m + 2) tanm+1 x + c (c) (d) (m + 1) tanm+1 x + c

Solution & Step-by-Step Answer:

(a)

Question 5 Maharashtra Board Solution

∫tan(sin-1 x). dx = (a) (b) (c) (d)

Solution & Step-by-Step Answer:

(d)

Hint: sin^-1x =

Question 6 Maharashtra Board Solution

(a) x cot() + c (b) -x cot() + c (c) cot() + c (d) x tan() + c

Solution & Step-by-Step Answer:

(b) -x cot() + c

Question 7 Maharashtra Board Solution

If f(x) = , g(x) = , then ∫f(x). g(x). dx = (a) (b) (c) (d)

Solution & Step-by-Step Answer:

(a)

Question 8 Maharashtra Board Solution

If ∫tan3 x. sec3 x. dx = () secm x – () secn x + c, then (m, n) = (a) (5, 3) (b) (3, 5) (c) (d) (4, 4)

Solution & Step-by-Step Answer:

(a) (5, 3)

Hint: ∫tan³x. sec³x dx
= ∫sec²x. tan²x. sec x tan x dx
= ∫sec²x (sec²x – 1) sec x tan x dx
Put sec x = t.

Question 9 Maharashtra Board Solution

(a) log(cosec x – cot x) + tan() + c (b) sin 2x – cos x + c (c) log(sec x + tan x) – cot() + c (d) cos 2x – sin x + c

Solution & Step-by-Step Answer:

Question 10 Maharashtra Board Solution

(a) (b) (c) (d)

Solution & Step-by-Step Answer:

(b)

Question 11 Maharashtra Board Solution

(a) (b) (c) (d) x e-x + c

Solution & Step-by-Step Answer:

(a)

Question 12 Maharashtra Board Solution

∫sin(log x). dx = (a) [sin(log x) – cos(log x)] + c (b) [sin(log x) + cos(log x)] + c (c) [cos(log x) – sin(log x)] + c (d) [cos(log x) – sin(log x)] + c

Solution & Step-by-Step Answer:

(a) [sin(log x) – cos(log x)] + c

Question 13 Maharashtra Board Solution

∫xx (1 + log x). dx = (a) (1 + log x)2 + c (b) x2x + c (c) xx log x + c (d) xx + c

Solution & Step-by-Step Answer:

(d) xx + c

Hint: (xx) = x^x(1 + log x)

Question 14 Maharashtra Board Solution

(a) (b) (c) (d)

Solution & Step-by-Step Answer:

(c)

Hint:
=
=
Put tan x = t.

Question 15 Maharashtra Board Solution

(a) sin 2x + c (b) cos 2x + c (c) tan 2x + c (d) 2 sin 2x + c

Solution & Step-by-Step Answer:

(a) sin 2x + c

Question 16 Maharashtra Board Solution

(a) log(tan x – ) + c (b) sin-1 (tan x) + c (c) 1 + sin-1 (cot x) + c (d) log(tan x + ) + c

Solution & Step-by-Step Answer:

(d) log(tan x + ) + c

Question 17 Maharashtra Board Solution

(a) (b) x(1 + log x) + c (c) (d)

Solution & Step-by-Step Answer:

(a)

Question 18 Maharashtra Board Solution

∫[sin(log x) + cos(log x)]. dx = (a) x cos(log x) + c (b) sin(log x) + c (c) cos(log x) + c (d) x sin(log x) + c

Solution & Step-by-Step Answer:

(d) x sin(log x) + c

Question 19 Maharashtra Board Solution

(a) tan x – x + c (b) x + tan x + c (c) x – tan x + c (d) -x – cot x + c

Solution & Step-by-Step Answer:

Question 20 Maharashtra Board Solution

(a) (b) (c) (d)

Solution & Step-by-Step Answer:

(a)

II. Integrate the following with respect to the respective variable:

Question 1 Maharashtra Board Solution

(x – 2)2 √x

Solution & Step-by-Step Answer:

Question 2 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 3 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 4 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 5 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 6 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 7 Maharashtra Board Solution

cos 3x cos 2x cos x

Solution & Step-by-Step Answer:

Question 8 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 9 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Let I =

III. Integrate the following w.r.t. x:

Question 1 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 2 Maharashtra Board Solution

cot-1 (1 – x + x2)

Solution & Step-by-Step Answer:

Question 3 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 4 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 5 Maharashtra Board Solution

log(1 + cos x) – x tan()

Solution & Step-by-Step Answer:

Question 6 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 7 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 8 Maharashtra Board Solution

log(log x) + (log x)-2

Solution & Step-by-Step Answer:

Question 9 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 10 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 11 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 12 Maharashtra Board Solution

log(x2 + 1)

Solution & Step-by-Step Answer:

Question 13 Maharashtra Board Solution

e2x sin x cos x

Solution & Step-by-Step Answer:

Question 14 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 15 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 16 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 17 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 18 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 19 Maharashtra Board Solution

Solution & Step-by-Step Answer:

Question 20 Maharashtra Board Solution

sec4 x cosec2 x

Solution & Step-by-Step Answer:

Chapter 3 Indefinite Integration Miscellaneous Exercise 3 Solutions