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 + x^{2})^{3/2} + C

(C) \(\frac{2}{3}\)x(1 + x^{2})^{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.