RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9

Rajasthan Board RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 Textbook Exercise Questions and Answers.

Rajasthan Board RBSE Solutions for Class 12 Maths in Hindi Medium & English Medium are part of RBSE Solutions for Class 12. Students can also read RBSE Class 12 Maths Important Questions for exam preparation. Students can also go through RBSE Class 12 Maths Notes to understand and remember the concepts easily.

RBSE Class 12 Maths Solutions Chapter 7 Integrals Ex 7.9

Question 1.
\(\int_{-1}^{1}(x + 1)\) dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 1

RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9

Question 2.
\(\int_{2}^{3} \frac{1}{x}\) dx
Answer:
Let
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 2
= log 3 - log 2 = log \(\frac{3}{2}\)

Question 3.
\(\int_{1}^{2}\) (4x3 - 5x2 + 6x + 9) dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 3

Question 4.
\(\int_{0}^{\pi / 4}\) sin 2x dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 4

RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9

Question 5.
\(\int_{0}^{\pi / 2}\) cos 2x dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 5

Question 6.
\(\int_{4}^{5}\) ex dx
Answer:
Let I = \(\int_{4}^{5}\) ex dx
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 6
= e5 - e4 = e4 (e - 1)

Question 7.
\(\int_{0}^{\pi / 4}\) tan x dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 7
= (log sec\(\frac{\pi}{4}\) - log sec 0)
= (log √2 - log 1)
= log 21/2 - 0 = \(\frac{1}{2}\)log 2

RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9

Question 8.
\(\int_{\pi / 6}^{\pi / 4}\) cosec x dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 8

Question 9.
\(\int_{0}^{1} \frac{d x}{\sqrt{1-x^{2}}}\)
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 9

Question 10.
\(\int_{0}^{1} \frac{d x}{1+x^{2}}\)
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 10

RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9

Question 11.
\(\int_{2}^{3} \frac{d x}{x^{2}-1}\)
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 11

Question 12.
\(\int_{0}^{\pi / 2}\) cos2 x dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 12

Question 13.
\(\int_{2}^{3} \frac{x d x}{x^{2}+1}\)
Answer:
Let I = \(\int_{2}^{3} \frac{x d x}{x^{2}+1}\)
Putting x2 + 1 = t
⇒ 2x dx = dt ⇒ x dx = \(\frac{1}{2}\) dt
When x = 3, then t = 32 + 1 = 10
When x = 2, then t = 22 + 1 = 5
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 13

RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9

Question 14.
\(\int_{0}^{1} \frac{2 x+3}{5 x^{2}+1}\) dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 14

Question 15.
\(\int_{0}^{1}\) xex2
Answer:
Let I = \(\int_{2}^{3}\) xex2 dx
Putting x2 = t
⇒ 2x dx = dt ⇒ x dx = \(\frac{1}{2}\) dt
When x = 1, then t = 1
When x = 0, then t = 0
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 15

Question 16.
\(\int_{1}^{2} \frac{5 x^{2}}{x^{2}+4 x+3}\) dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 16
⇒ 20x + 15 = A(x + 1) + B(x + 3)
Puffing x = - 1
20(- 1) + 15 = A(- 1 + 1) + B(- 1 + 3)
⇒ - 5 = 0 + 2B
∴ B = - \(\frac{5}{2}\)
Putting x = - 3
20(- 3) + 15 = A(- 3 + 1) + B(- 3 + 3)
⇒ - 60 + 15 = - 2A
⇒ - 45 = - 2A
∴ A = \(\frac{45}{2}\)
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 17

RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9

Question 17.
\(\int_{0}^{\pi / 4}\) (2 sec2 x + x3 + 2) dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 18

Question 18.
\(\int_{0}^{\pi}\) (sin2\(\frac{x}{2}\) - cos2\(\frac{x}{2}\)) dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 19

Question 19.
\(\int_{0}^{2} \frac{6 x+3}{x^{2}+4}\) dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 20

Question 20.
\(\int_{0}^{1}\left(x e^{x}+\sin \frac{\pi x}{4}\right)\) dx
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 21

RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9

Question 21.
\(\int_{1}^{\sqrt{3}} \frac{d x}{1+x^{2}}\) equals:
(A) \(\frac{\pi}{3}\)
(B) \(\frac{2 \pi}{3}\)
(C) \(\frac{\pi}{6}\)
(D) \(\frac{\pi}{12}\)
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 22
Hence, (D) is the correct answer.

Question 22.
\(\int_{0}^{2 / 3} \frac{d x}{4+9 x^{2}}\) equals:
(A) \(\frac{\pi}{6}\)
(B) \(\frac{\pi}{12}\)
(C) \(\frac{\pi}{24}\)
(D) \(\frac{\pi}{4}\)
Answer:
RBSE Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.9 23
Hence, (C) is the correct answer.

Bhagya
Last Updated on Nov. 3, 2023, 9:36 a.m.
Published Nov. 2, 2023