RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

Rajasthan Board RBSE Class 12 Maths Chapter 9 समाकलन Ex 9.5

निम्न फलनों का x के सापेक्ष समाकलन कीजिए-

प्रश्न 1.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 2.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 3.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 4.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 5.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 6.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
sin x = t
cos x dx = dt
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
= tan-1(t+2)+c
= tan-1(sin x+2)+c

प्रश्न 7.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
x – 3 = A\(\frac { d }{ dx }\)(x² + 2x – 4) + B
⇒ x – 3 = A(2x – 2) + B
⇒ x – 3 = 2Ax + (2A + B)
तुलना करने पर,
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 8.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
3x + 1 = A\(\frac { d }{ dx }\)(2x² – 2x + 3) + B
⇒ 3x + 1 = A(4x – 2) + B
⇒ 3x + 1 = 4Ax – 2A + B
तुलना करने पर,
4A = 3 ⇒ \(A=\frac { 3 }{ 4 }\)
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 9.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
माना x + 1 = A\(\frac { d }{ dx }\)(x² + 4x + 5) + B
⇒ x + 1 = A(2x + 4) + B
⇒ 2A = 1 ⇒ A = 1/2
⇒ 4A + B = 1 ⇒ B = -1
∴ x + 1 = \(\frac { 1 }{ 2 }\) (2x + 4) – 1
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 10.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
माना sinx = t
cos x dx = dt
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 11.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
(e-2x से हर व अंश में गुणा करने पर)
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
t = At + 2A + Bt + B
t = (A +B)t + (2A + B)
तुलना से, A + B = 1
2A + B = 0
B = -2A
A + (-2A) = 1
A – 2A = 1
– 2A = 1
– A = 1 या A = -1
B = -2 x (- 1) = 2 या B = 2
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 12.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 13.
<img src="http://www.rbseguide.com/wp-content/uploads/2019/05/RBSE-Solutions-for-Class-12-Maths-Chapter-9-Ex-9.5-12.1.png" alt="RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5" width="321" height="388" class="alignnone size-full wp-image-21269" />
हल :
<img src="http://www.rbseguide.com/wp-content/uploads/2019/05/RBSE-Solutions-for-Class-12-Maths-Chapter-9-Ex-9.5-12.1.png" alt="RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5" width="321" height="388" class="alignnone size-full wp-image-21269" />

प्रश्न 14.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 15.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 16.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
माना
x² – 2x +4 = t
(2x – 2) = t
2(x – 1)dx = dt
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 17.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
x + 1 = A\(\frac { d }{ dx }\)(x² – x + 1) + B
x + 1 = A(2x – 1) + B
x + 1 = 2Ax – A + B
तुलना करने पर,
2A = 1, A = 1/2
– A + B = 1
⇒ B = \(\frac { 3 }{ 2 }\)
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 18.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
x + 3 = A\(\frac { d }{ dx }\)(x² + 2x + 2) + B
⇒ x + 3 = A(2x + 2) + B
⇒ x + 3 = 24x + 2A + B
तुलना करने पर,
2A = 1, A = \(\frac { 1 }{ 2 }\)
2A + B = 3, B = 2
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 19.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 20.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 21.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

प्रश्न 22.
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
हल :
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5
माना ex = t
ex dx = dt
RBSE Solutions for Class 12 Maths Chapter 9 समाकलन Ex 9.5

RBSE Solutions for Class 12 Maths