English
Hindi

Question

Download Solution PDF

If f(0) = 1 and f(1) = 2.72, then the approximate value of trapezoidal rule gives 

This question was previously asked in
BPSC Asstt. Prof. ME Held on Nov 2015 (Advt. 22/2014)
Download PDF Attempt in App
View all BPSC Assistant Professor Papers >
  1. 3.72 
  2. 1.76
  3. 0.86
  4. 1.86

Answer (Detailed Solution Below)

Option 4 : 1.86

Detailed Solution

Download Solution PDF

Concept:

where, b = upper limit, a = lower limit, h = step size

According to the trapezoidal rule

Calculation:

Given:

f(0) = 1, f(1) = 2.72 and h = 1, ∴ n = 1.

x x0 = 0 x1 = 1
y = f(x) y0 = 1 y1 = 2.72

Download Solution PDF
Latest BPSC Assistant Professor Updates

Last updated on Jun 23, 2025

-> The Document Verification for BPSC Assistant Professor (Advt. No. 04/2025 to 28/2025) will be conducted between 7th July 2025 to 24th July 2025

-> The BPSC Assistant Professor Notification 2025 was released for 1711 vacancies under Speciality (Advt. No.04/2025 to 28/2025).

-> The recruitment is ongoing for 220 vacancies (Advt. No. 01/2024 to 17/2024).

-> The salary under BPSC Assistant Professor Recruitment is approximately Rs 15600-39100 as per Pay Matrix Level 11. 

-> The selection is based on the evaluation of academic qualifications &  work experience and interview.

-> Prepare for the exam using the BPSC Assistant Professor Previous Year Papers. For mock tests attempt the BPSC Assistant Professor Test Series.

Exams Tests Super Practice

More Solutions of Integral Equations Questions

Q1.Which order of Polynomials can best be integrated using Trapezoidal Rules?
Q2.Consider the definite integral \(\int^2_1(4x^2+2x+6)dx\) Let Ie be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is Is. The percentage error is defined as e = 100 × (Ie - Is)/Ie The value of e is
Q3.The value of \(\int_0^6{\frac{dx}{1+x^2}}\) by Simpson's \(\frac{1}{3}\) rule is
Q4.The table below gives values of function F(x) obtained for values of x at intervals of 0.25. x 0 0.25 0.5 0.75 1.0 F(x) 1 0.9412 0.8 0.64 0.50 The value of the integral of the function between the limits 0 to 1 using Simpson's rule is
Q5.The estimate of \(\int_{0.5}^{1.5}\dfrac{dx}{x}\) obtained using Simpson's rule with three-point function evaluation exceeds the exact value by
Q6.Find the magnitude of the error (correct to two decimal places) in the estimation of the following integral using Simpson’s 1/3 Rule. Take the step length as 1. _______ \(\displaystyle\int_0^4 \left( {{{\rm{x}}^4} + 10} \right){\rm{\;dx}} \)
Q7.Using the Simpson’s 1/3rd rule, the value of ∫ydx computed, for the data given below, is ________.       x            1          3          5     y 2 6 4
Q8.In numerical integration using Simpson’s rule, the approximating function in the interval is a
Q9.Match of the following: a Newton- Raphson I I. f(x) is a linear function of ‘x’ b Simpson’s 1/3rd rule II II. The number of intervals; must be even c Trapezoidal rule III III. Diagonal matrix d Gauss Elimination IV IV. Solution of algebraic and transcendental equations e Gauss-Jordan method V V. Forward elimination and Backward substitution Select the correct response.
Q10.In order to evaluate the integral  \(\displaystyle\int_{{0}}^{{1}} e^xdx \) with Simpson’s 1/3rd rule, values of the function ex are used at x = 0.0, 0.5 and 1.0. The absolute value of the error of numerical integration is

More Numerical Methods Questions

Q1.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q2.The rate of convergence of Newton Raphson method is :
Q3.If the value of the approximate solution of the initial value problem   \(\rm \left\{\begin{matrix}y'(x)=x(y(x)+1), &x\in R\\\ y(0)=β \end{matrix}\right.\) at x = 0.2 using the forward Euler method with step size 0.1 is 1.02, then the value of β is 
Q4.The iterative formula to find the root of the equation f(x) = x3 - 5x + 7 = 0 by the Newton Raphson method is ______.
Q5.In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to-
Q6.If \(\frac{dy}{dx}\) = x - y2 and y(0) = 1, then y(0.1) correct upto two decimal places (approx.) is:
Q7.In which of the following categories can we put Bisection method?
Q8.Which order of Polynomials can best be integrated using Trapezoidal Rules?
Q9.Consider the differential equation \(\rm \frac{dy}{dx}=4(x+2)-y \) For the initial condition y = 3 at x = 1, the value of 𝑦 at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is _________. (round off to one decimal place)
Q10.Consider the following recursive iteration scheme for different values of variable P with the initial guess x1 = 1. \(x_{n+1}=\frac{1}{2}\left(x_n+\frac{P}{x_n}\right)\), n = 1, 2, 3, 4, 5 For P = 2, x5 is obtained to be 1.414, rounded-off to three decimal places. For P = 3, x5 is obtained to be 1.732, rounded-off to three decimal places. If P = 10, the numerical value of x5 is ________. (round off to three decimal places)
Suggested Test Series
View All >
71st BPSC CCE (Preliminary) Test Series 2025
222 Total Tests with 1 Free Tests
Start Free Test
70th BPSC CCE Mock Test Series 2024
288 Total Tests with   5 Free Tests
Start Free Test

MPSC AE Important Links

ResultCut offEligibility CriteriaSyllabus and Exam PatternSelection ProcessSalary and Job Profile

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
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 joy vip teen patti gold teen patti club apk