GSEB Solutions Class 12 Maths Chapter 7 Integrals Ex 7.723

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.7 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.7

Integrate the following functions:
Question 1.
$\sqrt{4-x^{2}}$
Solution:

Question 2.
$\sqrt{1-4x^{2}}$
Solution:

Question 3.
$\sqrt{x^{2}+4 x+6}$
Solution:

Question 4.
$\sqrt{x^{2}+4 x+1}$
Solution:

Question 5.
$\sqrt{1-4 x-x^{2}}$
Solution:

Question 6.
$\sqrt{x^{2}+4 x-5}$
Solution:

Question 7.
$\sqrt{1+3 x-x^{2}}$
Solution:

Question 8.
$\sqrt{x^{2}+3 x}$
Solution:

Question 9.
$\sqrt{1+\frac{x^{2}}{9}}$
Solution:

Choose the correct answers in questions 10 and 11:
Question 10.
∫ $\sqrt{1+x^{2}}$ dx is equal to
(A) $\frac{x}{2}$ $\sqrt{1+x^{2}}$ + $\frac{1}{2}$ log|x + $\sqrt{1+x^{2}}$| + C
(B) $\frac{2}{3}$(1 + x²)^3/2 + C
(C) $\frac{2}{3}$x(1 + x²)^3/2 + C
(D) $\frac{x^{2}}{2}$$\sqrt{1+x^{2}}$ + $\frac{x^{2}}{2}$log|x + $\sqrt{1+x^{2}}$| + C
Solution:
We have:

∴ Part (A) is the correct answer.

Question 11.
∫ $\sqrt{x^{2}-8 x+7}$ dx is equal to
(A) $\frac{1}{2}$(x – 4)$\sqrt{x^{2}-8 x+7}$ + 9log |x – 4 + $\sqrt{x^{2}-8 x+7}$| + C
(B) $\frac{1}{2}$(x + 4)$\sqrt{x^{2}-8 x+7}$ + 9log |x + 4 + $\sqrt{x^{2}-8 x+7}$| + C
(C) $\frac{1}{2}$(x – 4)$\sqrt{x^{2}-8 x+7}$ – 3$\sqrt{2}$log |x – 4 + $\sqrt{x^{2}-8 x+7}$| + C
(D) $\frac{1}{2}$(x – 4)$\sqrt{x^{2}-8 x+7}$ – $\frac{9}{2}$log |x – 4 + $\sqrt{x^{2}-8 x+7}$| + C
Solution:

∴ Part (D) is the correct answer.