GSEB Solutions Class 12 Maths Chapter 7 Integrals Ex 7.9

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.9 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.9

Evaluate the following definite integrals:
Question 1.
$\int_{-1}^{1}$ (x + 1)dx
Solution:

Question 2.
$\int_{2}^{3}$ $\frac{1}{x}$ dx
Solution:

= log 3 – log 2 = log $\frac{3}{2}$.

Question 3.
$\int_{1}^{2}$ (4x³ – 5x² + 6x + 9) dx
Solution:

Question 4.
$\int_{0}^{\frac{\pi}{4}}$ sin 2x dx
Solution:

= – $\frac{1}{2}$(cos $\frac{π}{2}$ – cos 0) = $\frac{1}{2}$

Question 5.
$\int_{0}^{\frac{\pi}{2}}$ cos 2x dx
Solution:

= $\frac{1}{2}$[sin π – sin 0] = $\frac{1}{2}$(0 – 0) = 0.

Question 6.
$\int_{4}^{5}$ e^x dx
Solution:

= e⁵ – e⁴ = e⁴(e – 1).

Question 7.
$\int_{0}^{\frac{\pi}{4}}$ tanx dx
Solution:

Question 8.
$\int_{\frac{\pi}{6}}^{\frac{\pi}{4}}$ cosec x dx
Solution:

Question 9.
$\int_{0}^{1}$ $\frac{dx}{\sqrt{1-x^{2}}}$
Solution:

Question 10.
$\int_{0}^{1}$ $\frac{dx}{\sqrt{1+x^{2}}}$
Solution:

Question 11.
$\int_{2}^{3}$ $\frac{dx}{x^{2}-1}$
Solution:

Question 12.
$\int_{0}^{\frac{\pi}{2}}$ cos² x dx
Solution:

Question 13.
$\int_{2}^{3}$ $\frac{x d x}{x^{2}+1}$
Solution:

Question 14.
$\int_{0}^{1}$ $\frac{2 x+3}{5 x^{2}+1}$ dx
Solution:

Question 15.
$\int_{0}^{1}$ x e^x2 dx
Solution:

Question 16.
$\int_{1}^{2}$ $\frac{5 x^{2}}{x^{2}+4 x+3}$ dx
Solution:

Question 17.
$\int_{0}^{\frac{\pi}{4}}$ (2sec² x + x³ + 2) dx
Solution:

Question 18.
$\int_{0}^{π}$(sin² $\frac{x}{2}$ – cos² $\frac{x}{2}$)dx
Solution:

Question 19.
$\int_{0}^{2}$ $\frac{6 x+3}{x^{2}+4}$ dx
Solution:

Question 20.
$\int_{0}^{1}$(xe^x + sin $\frac{πx}{2}$) dx
Solution:

Choose the correct answers in questions 21 and 22:
21. $\int_{1}^{\sqrt{3}}$ equals
(A) $\frac{π}{3}$
(B) $\frac{2π}{3}$
(C) $\frac{π}{6}$
(D) $\frac{π}{12}$
Solution:

∴ Part (D) is the correct answer.

Question 22.
$\int_{-6}^{\frac{2}{3}} \frac{d x}{4+9 x^{2}}$ equals
(A) $\frac{π}{6}$
(B) $\frac{π}{12}$
(C) $\frac{π}{24}$
(D) $\frac{π}{4}$
Solution:

∴ Part (C) is the correct answer.