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

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.