English
Hindi

Question

Download Solution PDF

 f(x) dx is equal to

  1.  f(x − c)dx
  2.  f(x + c)dx
  3.  f(x) dx
  4.  f(x) dx

Answer (Detailed Solution Below)

Option 2 :  f(x + c)dx

Detailed Solution

Download Solution PDF

Concept:

​ → (1)​

Calculation: 

Given: ​​​​

Let x = t + c

⇒ dx = dt

Also when x = a + c ⇒ t = a

And x = b + c ⇒ t = b

Therefore 

From (1) By replacing t by x we get,

The correct answer is option 2.

Download Solution PDF
Exams Tests Super Practice

More Properties of Definite Integrals Questions

Q1.What is \(\rm \int_{-\pi}^\pi g(t)dt\) equal to
Q2.\(\displaystyle \int_{0}^{\pi / 2} \frac{\sqrt{\tan x}}{\sqrt{\tan x}+\sqrt{\cot x}} d x\) is
Q3.Which one of the following options represents the given graph?
Q4.The functional I(y(x)) = \(\rm\displaystyle\int_a^b\)(y2 + \(\rm y^{\prime^2}\) + 2y sin x)dx has which of the following extremal with C1 and C2 as arbitrary constants?
Q5.The value of \(\int_0^{π / 2} \frac{\sqrt{\cos x}}{\sqrt{(\sin x)}+\sqrt{(\cos x)}} d x\) is
Q6.\(\rm\displaystyle\int_{−1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1}\) dx is equal to
Q7.If f and g are continuous functions in [0, 1] satisfying f(x) = f(a − x) and g(x) + g(a − x) = a, then \(\rm \displaystyle\int_0^a\) f(x) . g(x) dx is equal to
Q8.\(\rm \displaystyle\int_{a+c}^{b+c}\) f(x) dx is equal to
Q9.\(\int_{\rm{0}}^{\rm{1}} {{\rm{log}}\left( {\frac{{\rm{1}}}{{\rm{x}}}{\rm{ - 1}}} \right)} \)dx equals

More Integral Calculus Questions

Q1.What is U(x) V(x) equal to? 
Q2.What is |U2(x) - V2(x)| equal to?
Q3.What is I equal to?
Q4.What is \(\rm \int_0^{\pi/2}\frac{d(x)}{g(x)}\) equal to
Q5.What is \(\rm \int_{-\pi}^\pi g(t)dt\) equal to
Q6.Consider the following statements : I. f(t) is an odd function. Il. g(t) is an odd function. Which of the statements given above is/are correct?  
Q7.What is \(\rm \int_h^3f(x)dx\) equal to
Q8.What is \(\rm \int_0^2f(x)dx\) equal to
Q9.What is the area of the parabola bounded by the latus rectum? 
Q10.What is the value of k? 

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： real teen patti teen patti game online teen patti real