Civil Engineering (CE) Exam  >  Civil Engineering (CE) Tests  >  Engineering Mathematics  >  Test: Solution Integrals - Civil Engineering (CE) MCQ

Test: Solution Integrals - Civil Engineering (CE) MCQ


Test Description

5 Questions MCQ Test Engineering Mathematics - Test: Solution Integrals

Test: Solution Integrals for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation. The Test: Solution Integrals questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Solution Integrals MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Solution Integrals below.
Solutions of Test: Solution Integrals questions in English are available as part of our Engineering Mathematics for Civil Engineering (CE) & Test: Solution Integrals solutions in Hindi for Engineering Mathematics course. Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free. Attempt Test: Solution Integrals | 5 questions in 15 minutes | Mock test for Civil Engineering (CE) preparation | Free important questions MCQ to study Engineering Mathematics for Civil Engineering (CE) Exam | Download free PDF with solutions
Test: Solution Integrals - Question 1

The number of integral solutions of  is

Detailed Solution for Test: Solution Integrals - Question 1


4x + 8 ≥ x2 + 8

∴ x2 – 4x ≤ 0

x(x – 4) ≤ 0 → (1)

Clearly the integral solution of (1) are 0, 1, 2, 3 and 4

∴ Total 5 values of x satisfies (1)

Test: Solution Integrals - Question 2

 where c is the upper half of the circle |z| = 1.

Detailed Solution for Test: Solution Integrals - Question 2

Given counter c is the circle, |z| = 1

⇒  z = e ⇒ dz = ie

Now, for upper half of the circle, 0 ≤ θ ≤ π

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Solution Integrals - Question 3

Evaluate the line integral ⁡(x + 4iy2)dz where c is the line x = 2y and x varies from 0 to 1 and z = x + iy

Detailed Solution for Test: Solution Integrals - Question 3

Calculation:

z = x + iy ⇒ dz = dx + i dy

given line is x = 2y ⇒ dy/dx = 1/2

lets substitute y in terms of x

I = ∫ x + i x2 (dx + i/2 dx) 

I = ∫ x dx + i/2 x dx + i x2 dx - x2/2 dx

Test: Solution Integrals - Question 4

Evaluate along the straight line joining the points (0, 0) and (3, 1)

Detailed Solution for Test: Solution Integrals - Question 4

Concept:

Integral of a complex function f(z) is given

∫ f(z) dz = ∫ (udx -vdy) + i ∫ (vdx + udy)

Noting f(z) = u(x, y) + i v(x, y) and dz = dx + i dy;

Calculation:

Given Along the straight line joining the points (0, 0) and (3, 1);

The equation of straight line will be x = 3y

⇒ dx = 3 dy ⇒ dz = (3 + i) dy;

Along the line x = 3y, the complex number z will be

z = x + iy = 3y + iy = (3 + i) y

Substituting both in the integral,

Test: Solution Integrals - Question 5

The value of where contour D is |z| = 2

Detailed Solution for Test: Solution Integrals - Question 5

 has its poles at z = -1

and contour |z| = 2 is a circle of radius 2, centre (0, 0)

So

65 videos|120 docs|94 tests
Information about Test: Solution Integrals Page
In this test you can find the Exam questions for Test: Solution Integrals solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Solution Integrals, EduRev gives you an ample number of Online tests for practice

Top Courses for Civil Engineering (CE)

65 videos|120 docs|94 tests
Download as PDF

Top Courses for Civil Engineering (CE)