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

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.