English
Hindi

Question

Download Solution PDF

 is equal to

This question was previously asked in
UP TGT Mathematics 2016 Official Paper
Download PDF Attempt in App
View all UP TGT Papers >

Answer (Detailed Solution Below)

Option 2 :
Free Tests
View all Free tests >
Free
UP TGT Hindi FT 1
125 Qs. 500 Marks 120 Mins
Start Now

Detailed Solution

Download Solution PDF

Formula:

Calculation:

Let 

⇒ 

⇒ 

⇒ 

The above integrand is of the form 

 

 

Download Solution PDF
Latest UP TGT Updates

Last updated on May 6, 2025

-> The UP TGT Exam for Advt. No. 01/2022 will be held on 21st & 22nd July 2025.

-> The UP TGT Notification (2022) was released for 3539 vacancies.

-> The UP TGT 2025 Notification is expected to be released soon. Over 38000 vacancies are expected to be announced for the recruitment of Teachers in Uttar Pradesh. 

-> Prepare for the exam using UP TGT Previous Year Papers.

Exams Tests Super Practice

More Indefinite Integrals Questions

Q1.If ∫(cos x - sin x)/\(\rm \sqrt{8-\sin 2x)}\) dx = a sin-1(sin x + cos x)/b + c where c is a constant of integration, then the ordered pair (a, b) is equal to:
Q2.Let \(\mathrm{I}(x)=\int \frac{(x+1)}{x\left(1+x e^x\right)^2} d x, x>0 . \quad \lim _{x \rightarrow \infty} \mathrm{I}(x)=0\), then I(1) is equal to
Q3.\(\rm \int\frac{2x+3}{x^3+x^2-2x}dx=?\)
Q4.\(\rm \int\frac{e^{tan^{-1}x}}{1+x^2}dx=?\)
Q5.The value of \(\int \frac{x^{\frac{3}{2}}}{\sqrt{1+x^5}} d x\) is:
Q6.If \(\int \frac{\sqrt{4+x^2}}{x^6} d x\) = \(\frac{A\left(4+x^2\right)^{3 / 2}\left(B x^2-6\right)}{x^5}+C\), then A is:
Q7.The value of \(\int \frac{1}{2 x^2+x-3} d x\) is:
Q8.Integrate \(\frac{1}{x\left(x^{n}+1\right)}\) with respect to x.
Q9.An appropriate substitution for the integral \(\int \frac{1+x^{1 / 2}}{1+x^{1 / 3}} d x \) is
Q10.\(\int\frac{x^2-1}{x^4+x^2+1}dx = ?\)

More Integral Calculus Questions

Q1.If ∫(cos x - sin x)/\(\rm \sqrt{8-\sin 2x)}\) dx = a sin-1(sin x + cos x)/b + c where c is a constant of integration, then the ordered pair (a, b) is equal to:
Q2.The area (in sq. units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is:
Q3.The area of the region, enclosed by the circle x2 + y2 = 2 which is not common to the region bounded by the parabola y2 = x and the straight line y = x is
Q4.The area of the region: R{(x, y): 5x2 ≤ y ≤ 2x2 + 9} is:
Q5.The value of the integral, \(\int_1^3\left[x^2-2 x-2\right] d x\) where [x] denotes the greatest integer less than or equal to x , is :
Q6.Let the locus of the centre (α, β), β > 0, of the circle which touches the circle x2 + (y – 1)2 = 1 externally and also touches the x - axis be L. Then the area bounded by L and the line y = 4 is :
Q7.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
Q8.The area of the region given by A = {(x, y ); x2 ≤ y ≤ min {x + 2, 4 - 3x}} is
Q9.Let \(f(x) = \left\lbrace \begin{matrix} -2, & -2 \le x \le 0 \\\ x - 2, & 0 < x \le 2 \end{matrix} \right.\) and h(x) = f(|x|) + |f(x)|. Then \(\int_{-2}^2 h(x) dx\) is equal to:
Q10.One of the points of intersection of the curves y = 1 + 3x - 2x2 and \(y = \frac{1}{x}\) is \(\left(\frac{1}{2}, 2 \right).\) Let the area of the region enclosed by these curves be \(\frac{1}{24}(ℓ \sqrt{5}+m) - n\log_e (1+\sqrt{5})\), where ℓ, m, n, ∈ N. Then ℓ + m + n is equal to
Suggested Test Series
View All >
UP TGT Mock Test Series 2025
444 Total Tests with 6 Free Tests
Start Free Test
Pedagogy for All Teaching Exams (Paper 1 & 2) - Let's Crack TET!
345 Total Tests with   3 Free Tests
Start Free Test

Airforce Group X Important Links

ResultEligibility CriteriaSalary and Job ProfileAdmit CardSyllabus and Exam PatternAnswer Key

More Mathematics Questions

Q1.log10 10000 = _______?
Q2.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
Q3.Match List I with List II:   List - I List - II (I) The number of solutions of the equation\((1 - \cos 2x)(\cos 2x + \cot^2 x) = 0\) where \(0 \le x \le 2\pi\) is (P) 4 (II) \(\tan 81^\circ - \tan 63^\circ - \tan 27^\circ + \tan 9^\circ\) equals (Q) 3 (III) The number of solutions of (x, y), which satisfy |y| = sin x and y = cos-1(cos x), where -2π ≤ x ≤ 2π is (R) 2 (IV) For the equation \(\cos^{-1}x + \cos^{-1}2x + \pi = 0\), the number of real solutions is (S) 1     (T) 0  
Q4.If Σn = 36, find n
Q5.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q6.The growth model for a population is Nt = N0ert where Nt is the population at time t, N0 is the initial population and r is the per capita growth rate. How long does it take for the population numbers to double?
Q7.Suppose that the growth rate of the number of individuals (N) in a population in an environment with a carrying capacity K is modelled as \(\frac{d N}{d t}=r N \frac{K-N}{K}\) where r is the per capita growth rate and t is time; r and K are positive constants. At which of the following values of N will the population growth rate be the maximum?
Q8.The shadow of a vertical pole, formed due to a nearby lamp which is at a height of 12 m, measures 4 m. If the lamp is moved horizontally 2 m further away from the pole, the length of the shadow measures 8 m. What is the height (in m) of the pole?
Q9.A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Out of these 16 number of cards, two cards are drawn at random. Find the probability that at least one of them is an ace :
Q10.If the equations 2x2 + kx - 5 = 0 and x2 - 3x - 4 = 0 have one root common, then find the value of k.
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： teen patti gold teen patti circle teen patti all app teen patti bonus teen patti customer care number