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.

\(\int_{1}^{2}\) (4x^{3} – 5x^{2} + 6x + 9) dx

Solution:

Question 4.

\(\int_{0}^{\frac{\pi}{4}}\) sin 2x dx

Solution:

= – \(\frac{1}{2}\)(cos \(\frac{Ï€}{2}\) – cos 0) = \(\frac{1}{2}\)

Question 5.

\(\int_{0}^{\frac{\pi}{2}}\) cos 2x dx

Solution:

= \(\frac{1}{2}\)[sin Ï€ – sin 0] = \(\frac{1}{2}\)(0 – 0) = 0.

Question 6.

\(\int_{4}^{5}\) e^{x} dx

Solution:

= e^{5} – e^{4} = e^{4}(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.

\(\int_{0}^{\frac{\pi}{2}}\) cos^{2} 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^{x}^{2} dx

Solution:

Question 16.

\(\int_{1}^{2}\) \(\frac{5 x^{2}}{x^{2}+4 x+3}\) dx

Solution:

Question 17.

\(\int_{0}^{\frac{\pi}{4}}\) (2sec^{2} x + x^{3} + 2) dx

Solution:

Question 18.

\(\int_{0}^{Ï€}\)(sin^{2} \(\frac{x}{2}\) – cos^{2} \(\frac{x}{2}\))dx

Solution:

Question 19.

\(\int_{0}^{2}\) \(\frac{6 x+3}{x^{2}+4}\) dx

Solution:

Question 20.

\(\int_{0}^{1}\)(xe^{x} + sin \(\frac{Ï€x}{2}\)) dx

Solution:

Choose the correct answers in questions 21 and 22:

21. \(\int_{1}^{\sqrt{3}}\) equals

(A) \(\frac{Ï€}{3}\)

(B) \(\frac{2Ï€}{3}\)

(C) \(\frac{Ï€}{6}\)

(D) \(\frac{Ï€}{12}\)

Solution:

âˆ´ Part (D) is the correct answer.

Question 22.

\(\int_{-6}^{\frac{2}{3}} \frac{d x}{4+9 x^{2}}\) equals

(A) \(\frac{Ï€}{6}\)

(B) \(\frac{Ï€}{12}\)

(C) \(\frac{Ï€}{24}\)

(D) \(\frac{Ï€}{4}\)

Solution:

âˆ´ Part (C) is the correct answer.