GSEB Solutions Class 12 Maths Chapter 7 Integrals Ex 7.4

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.4 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.4

Integrate the following functions:
Question 1.
\(\frac{3 x^{2}}{x^{6}+1}\)
Solution:

Question 2.
\(\frac{1}{\sqrt{1+4 x^{2}}}\)
Solution:

Question 3.
\(\frac{dx}{\sqrt{(2-x)^{2}+1}}\)
Solution:

Question 4.
\(\frac{dx}{\sqrt{9-25 x^{2}}}\)
Solution:

Question 5.
\(\frac{3 x}{1+2 x^{4}}\)
Solution:

Question 6.
\(\frac{x^{2}}{1-x^{6}}\)
Solution:

Question 7.
\(\frac{x-1}{\sqrt{x^{2}-1}}\)
Solution:

Question 8.
\(\frac{x^{2}}{\sqrt{x^{6}+a^{6}}}\)
Solution:

Question 9.
\(\frac{1}{\sqrt{7-6 x-x^{2}}}\)
Solution:

Question 10.
\(\frac{1}{\sqrt{x^{2}+2 x+2}}\)
Solution:

Question 11.
\(\frac{1}{9 x^{2}+6 x+5}\)
Solution:

Question 12.
\(\frac{1}{\sqrt{7-6 x-x^{2}}}\)
Solution:

Question 13.
\(\frac{1}{\sqrt{(x-1)(x-2)}}\)
Solution:

Question 14.
\(\frac{1}{\sqrt{8+3 x-x^{2}}}\)
Solution:

Question 15.
\(\frac{1}{\sqrt{(x-a)(x-b)}}\)
Solution:

Question 16.
\(\frac{4 x+1}{\sqrt{2 x^{2}+x-3}}\)
Solution:

Question 17.
\(\frac{x+2}{\sqrt{x^{2}-1}}\)
Solution:

Question 18.
\(\frac{5 x-2}{1+2 x+3 x^{2}}\)
Solution:

Question 19.
\(\frac{6 x+7}{\sqrt{(x-5)(x-4)}}\)
Solution:

Question 20.
\(\frac{x+2}{\sqrt{4 x-x^{2}}}\)
Solution:

Question 21.
\(\frac{x+2}{\sqrt{x^{2}+2 x+3}}\)
Solution:

Question 22.
\(\frac{x+3}{x^{2}-2 x-5}\)
Solution:

Question 23.
\(\frac{5 x+3}{\sqrt{x^{2}+4 x+10}}\)
Solution:

Choose the correct answers in the following questions 24 and 25:
Question 24.
∫\(\frac{d x}{x^{2}+2 x+2}\) equals
(A) x tan^-1(x + 1) + C
(B) tan^-1(x + 1) + C
(C) (x + 1) tan^-1x + C
(D) tan^-1x + C
Solution:
∫\(\frac{d x}{x^{2}+2 x+2}\) = ∫\(\frac{d x}{(x+1)^{2}+1}\) = tan^-1 (x + 1) + C
∴ Part (B) is the correct answer.

Question 25.
Let I = ∫\(\frac{d x}{\sqrt{9 x-4 x^{2}}}\) equals
(A) \(\frac{1}{9}\) sin^-1  (\(\frac{9x-8}{8}\)) + C
(B) \(\frac{1}{2}\) sin^-1 (\(\frac{8x-9}{9}\)) + C
(C) \(\frac{1}{3}\) sin^-1 (\(\frac{9x-8}{8}\)) + C
(D) \(\frac{1}{2}\) sin^-1 (\(\frac{9x-8}{8}\)) + C
Solution:

∴ Part (B) is the correct answer.