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.
∫ \(\sqrt{1+x^{2}}\) 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.