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Test: Improper Integrals - Civil Engineering (CE) MCQ


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10 Questions MCQ Test - Test: Improper Integrals

Test: Improper Integrals for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Test: Improper Integrals questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Improper Integrals MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Improper Integrals below.
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Test: Improper Integrals - Question 1

Integration of function is same as the ___________

Detailed Solution for Test: Improper Integrals - Question 1

Integration of function is same as the Joining many small entities to create a large entity.

Test: Improper Integrals - Question 2

Integration of (Sin(x) – Cos(x))ex is _______

Detailed Solution for Test: Improper Integrals - Question 2

Add constant automatically
Let f(x) = ex Sin(x)
∫ ex Sin(x)dx = -ex Cos(x) + ∫ ex Cos(x)dx
∫ ex Sin(x)d - ∫ ex Cos(x)dx = ∫ ex [Sin(x) - Cos(x)]dx
= -ex Cos(x).

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Test: Improper Integrals - Question 3

If differentiation of any function is zero at any point and constant at other points then it means?

Detailed Solution for Test: Improper Integrals - Question 3

Since slope of a function is given by dydx at that point. Hence, when dydx = 0 means slope of a function is zero i.e, parallel to x axis.
Function is not a constant function since it has finite value at other points.

Test: Improper Integrals - Question 4

Integration of function y = f(x) from limit x1 < x < x2 , y1 < y < y2, gives ___________

Detailed Solution for Test: Improper Integrals - Question 4

Integration of function y=f(x) from limit x1 < x < x2 , y1 < y < y2, gives area of f(x) within x1 < x < x2.

Test: Improper Integrals - Question 5

Find the value of ∫t(t + 3)(t + 2) dt, is?

Detailed Solution for Test: Improper Integrals - Question 5

Add constant automatically
Given, et = x ⇒ dx = et dt,
Given,

Let, z = ln⁡(x) ⇒ dz = dxx
⇒ 

Test: Improper Integrals - Question 6

 Find the value of  .

Detailed Solution for Test: Improper Integrals - Question 6

Add constant automatically
Given, 

Test: Improper Integrals - Question 7

Integration of (Sin(x) + Cos(x))ex is______________

Detailed Solution for Test: Improper Integrals - Question 7

Let f(x) = ex Sin(x)

∫ ex Sin(x)dx = ex Sin(x) – ∫ ex Cos(x)dx

∫ ex Sin(x)dx + ∫ ex Cos(x)dx = ∫ ex [Cos(x) + Sin(x)]dx

= ex Sin(x).

Test: Improper Integrals - Question 8

Value of ∫ Cos2 (x) Sin2 (x)dx.

Detailed Solution for Test: Improper Integrals - Question 8

Add constant automatically
Given,f(x) = 

Test: Improper Integrals - Question 9

If differentiation of any function is infinite at any point and constant at other points then it means ___________

Detailed Solution for Test: Improper Integrals - Question 9

Since slope of a function is given by dy⁄dx at that point.Hence,when dy⁄dx = ∞ means slope of a function is 90 degree i.e,parallel to y axis.

Test: Improper Integrals - Question 10

Find the value of ∫ ln⁡(x)x dx.

Detailed Solution for Test: Improper Integrals - Question 10

Add constant automatically
Given, 

Let, z = ln⁡(x)

⇒ 

⇒ 

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