GATE | GATE CS 2011 | Question 31
Given i=√-1, what will be the evaluation of the integral 
?
(A) 0
(B) 2
(C) -i
(D) i
Answer: (D)
Explanation:
![\int_{0}^{\pi/2} \frac{\cos x + i\sin x}{\cos x - i\sin x} dx \newline \newline = \int_{0}^{\pi/2} \frac{{e}^{ix}}{{e}^{-ix}} dx \hspace{0.2cm}= \int_{0}^{\pi/2} {e}^{2ix} dx \newline \newline = \frac{1}{2i} [{e}^{2ix}]^{\pi/2}_{0} \hspace{0.2cm} = \frac{1}{2i} [{e}^{i\pi} - {e}^{0}] \newline \newline = \frac{1}{2i} [\cos \pi + i\sin \pi - 1] \newline \newline = \frac{1}{2i}[-1 + 0 - 1] \times \frac{i}{i} = i](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-a12d7a161b7c1bd24c2d936e6157ec5e_l3.png "Rendered by QuickLaTeX.com")
.png)
Complete Interview Preparation
View Details
- GATE | GATE CS 2011 | Question 31
- GATE | GATE CS 2010 | Question 2
- GATE | GATE CS 2010 | Question 3
- GATE | GATE CS 2010 | Question 4
- GATE | GATE-CS-2009 | Question 1
- GATE | GATE-CS-2009 | Question 60
- GATE | GATE-CS-2014-(Set-1) | Question 65
- GATE | GATE-CS-2014-(Set-3) | Question 65
- GATE | GATE CS 2010 | Question 65
- GATE | GATE CS 2008 | Question 85
- GATE | GATE-CS-2005 | Question 76
- Database Management Systems | Set 8
- Database Management Systems | Set 9
- Database Management Systems | Set 10
- Database Management Systems | Set 2
- Database Management Systems | Set 3
- Database Management Systems | Set 4
- Database Management Systems | Set 5
- Database Management Systems | Set 6
- Database Management Systems | Set 7
- Database Management Systems | Set 11
- Database Management Systems | Set 1
- Introduction of DBMS (Database Management System) | Set 1
- Introduction of 3-Tier Architecture in DBMS | Set 2
- DBMS Architecture 2-Level, 3-Level
- GATE | GATE CS 2011 | Question 37
- Important Topics for GATE 2020 Computer Science
- GATE | GATE CS 2013 | Question 31
- GATE | GATE CS 1996 | Question 39
- GATE | GATE CS 2008 | Question 66
Improve Article
Save Article
Like Article
Article Contributed By :
Article Tags :
Writing code in comment? Please use ide.geeksforgeeks.org, generate link and share the link here.
.png)