Bengali
English
Hindi

Question

Download Solution PDF

সমাকলের মান নির্ণয় করুন,

যেখানে [x] , x এর চেয়ে ছোট বা সমান সর্বশ্রেষ্ঠ পূর্ণসংখ্যা নির্দেশ করে, হল: ।

  1. -4
  2. -5
  3. -√2 - √3 - 1
  4. -√2 - √3 + 1

Answer (Detailed Solution Below)

Option 3 : -√2 - √3 - 1

Detailed Solution

Download Solution PDF

গণনা:

প্রদত্ত, I =

⇒ I =

⇒

⇒ ধরি x - 1 = t ; dx = dt

⇒

⇒

⇒ I = -6 + (√2 - 1) + 2√3 - 2√2 + 6 - 3√3

⇒ I = - 1 - √2 - √3

∴ সমাকলের মান হল - 1 - √2 - √3.

সঠিক উত্তর বিকল্প 3

Download Solution PDF
‹‹ Previous Ques
Next Ques ››
Exams Tests Super Practice

More Definite Integrals Questions

Q1.What is I equal to?
Q2.What is \(\rm \int_0^{\pi/2}\frac{d(x)}{g(x)}\) equal to
Q3.What is \(\rm \int_h^3f(x)dx\) equal to
Q4.What is \(\rm \int_0^2f(x)dx\) equal to
Q5.The value of the integral \(\int_{-1}^{1} \int_{0}^{\sqrt{1-x^{2}}}\left(x^{2}+y^{2}\right)^{\frac{3}{2}} d y d x\) is:
Q6.Let \(I_{1}=\int_{0}^{1} \frac{\operatorname{cosec} x}{x} d x\) and \(I_{2}=\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{m} x}{x^{n}} d x\) then :
Q7.সমাকলের মান নির্ণয় করুন, \(\int_1^3\left[x^2-2 x-2\right] d x\) যেখানে [x] , x এর চেয়ে ছোট বা সমান সর্বশ্রেষ্ঠ পূর্ণসংখ্যা নির্দেশ করে, হল: ।
Q8.For any real number x, let [x] denote the largest integer less than equal to x. Let f be a real valued function defined on the interval [–10, 10] by \(f(x)=\left\{\begin{array}{c} x-[x], \text { if }[x] \text { is odd } \\ 1+[x]-x, \text { if }[x] \text { is even } \end{array}\right.\) Then the value of \(\frac{\pi^2}{10} \int_{-10}^{10} f(x) \cos \pi x d x\) is
Q9.\(\rm \int_{-\pi}^\pi \frac{2y(1+\sin y)}{1+\cos^2y}dy\) এর মান হল:
Q10.The integral \(\rm \int_0^{\frac{\pi}{4}}\frac{136\sin x}{3\sin x+5\cos x}\) is equal to:

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： mpl teen patti teen patti master old version master teen patti teen patti refer earn