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.