RB 12 Maths

RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1

RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1

Rajasthan Board RBSE Class 12 Maths Chapter 9 समाकलन Ex 9.1

प्रश्न 1.
निम्न फलनों का x के सापेक्ष समाकलन कीजिए

RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1

निम्न समाकलों के मान ज्ञात कीजिए
प्रश्न 2.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
= 5 ∫cos x dx – 3 ∫sin x dx + 2 ∫sec² x dx
= 5 sin x – 3( – cos x) + 2 tan x + c
= 5 sin x + 3 cos x + 2 tan x + c

प्रश्न 3.
<img src="http://www.rbseguide.com/wp-content/uploads/2019/05/RBSE-Solutions-for-Class-12-Maths-Chapter-9-Ex-9.1-2.png" alt="RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1" width="244" height="58" class="alignnone size-full wp-image-20523" />
हल:
<img src="http://www.rbseguide.com/wp-content/uploads/2019/05/RBSE-Solutions-for-Class-12-Maths-Chapter-9-Ex-9.1-2.png" alt="RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1" width="244" height="58" class="alignnone size-full wp-image-20523" />

प्रश्न 4.
∫(sec² x + cosec² x) dx
हल :
∫(sec² x + cosec² x) dx
= ∫sec² x + ∫cosec² dx
= tan x – cot x + c

प्रश्न 5.
∫(1 + x) √x dx
हल:
∫(1 + x) √x dx
<img src="http://www.rbseguide.com/wp-content/uploads/2019/05/RBSE-Solutions-for-Class-12-Maths-Chapter-9-Ex-9.1-2.png" alt="RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1" width="244" height="58" class="alignnone size-full wp-image-20523" />

प्रश्न 6.
∫ax da
हल:
∫ax da =
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1

प्रश्न 7.

हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1

प्रश्न 8.
 <img src="http://www.rbseguide.com/wp-content/uploads/2019/05/RBSE-Solutions-for-Class-12-Maths-Chapter-9-Ex-9.1-7.png" alt="" width="89" height="53" class="alignnone size-full wp-image-20534" />
हल:
 <img src="http://www.rbseguide.com/wp-content/uploads/2019/05/RBSE-Solutions-for-Class-12-Maths-Chapter-9-Ex-9.1-7.png" alt="" width="89" height="53" class="alignnone size-full wp-image-20534" />
= ∫(1 – sin x) dx
= ∫dx – ∫sin x dx
= x – (-cos x) + c
= x + cos x + c

प्रश्न 9.
∫sec x (sec x + tan x) dx
हल:
∫sec x (sec x + tan x) dx
= ∫sec² x dx + ∫sec x tan x dx
= tan x + sec x + c

प्रश्न 10.
∫(sin-1 x + cos-1 x) dx
हल:
∫(sin-1 x + cos-1 x) dx
 <img src="http://www.rbseguide.com/wp-content/uploads/2019/05/RBSE-Solutions-for-Class-12-Maths-Chapter-9-Ex-9.1-7.png" alt="" width="89" height="53" class="alignnone size-full wp-image-20534" />

प्रश्न 11.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
= x – 2 tan-1 x + c

प्रश्न 12.
∫ tan² x dx
हल:
∫ tan² x dx = ∫(sec²x – 1)dx
= ∫sec² – ∫dx
= tan x – x + c

प्रश्न 13.
∫cot² x dx
हल:
∫(cosec²x – 1)dx
= ∫cosec² dx – ∫dx
= – cot x – x + c

प्रश्न 14.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1

प्रश्न 15.
∫(tan²x – cot²x) dx
हल:
∫(tan²x – cot²x) dx
= ∫(sec²x – 1 – cosec²x + 1) dx
= ∫sec² x dx – ∫cosec² x dx
= tan x + cot x + c

प्रश्न 16.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
= ∫x – ∫sec² x dx + ∫tan x sec x dx
= x – tan x + sec x + c

प्रश्न 17.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
= ∫cosec² x dx + ∫cosec x cot x dx
= – cotx – cosec x + c

प्रश्न 18.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1

प्रश्न 19.
∫cot x (tan x – cosec x) dx
हल:
∫cot x (tan x – cosec x) dx
= ∫cot x tan x dx – ∫cot x cosec x dx
= ∫1 dx – ∫cosec x cot x dx
= x + cosec x + c

प्रश्न 20.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1

प्रश्न 21.
∫logx x dx
हल:
∫logx x dx
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
=∫1 dx
= x + c

प्रश्न 22.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
= √2∫cos x dx
= √2 sin x + c

प्रश्न 23.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
= ∫cosec² x dx – ∫sec² x dx
= – cot x – tan x + c

प्रश्न 24.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
हल:
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.1
= 3 ∫cosec x cot x dx + 4 ∫cosec² x dx
= – 3 cosec x + 4(-cotx) + c
= – 3 cosec x – 4 cotx + c

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