# GSEB Solutions Class 12 Maths Chapter 7 Integrals Ex 7.7

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.
âˆ« $$\sqrt{1+x^{2}}$$ 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:

âˆ´ Part (A) is the correct answer.

Question 11.
âˆ« $$\sqrt{x^{2}-8 x+7}$$ 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:

âˆ´ Part (D) is the correct answer.