Numerical Integration MCQs : Here you will find MCQ Questions related to "Numerical Integration" in Finite Element Method. These Numerical Integration MCQ Questions Will help you to improve your Finite Element Method knowledge and will prepare you for various Examinations like Competitive Exams, Placements, Interviews and other Entrance Exmaniations

Question 1

Numerical integration methods can generally be described as combining evaluations of the integrand to get an approximation to the integral. The integrand is evaluated at a finite set of points called?

A. quadrature point

B. composite point

C. midpoint

D. integration point

View Answer
**Ans **: D

**Explanation**: Numerical integration methods can generally be described as combining evaluations of the integrand to get an approximation to the integral. The integrand is evaluated at a finite set of points called integration points and a weighted sum of these values is used to approximate the integral.

Question 2

Numerical integration comprises a broad family of algorithms for calculating the numerical value of a?

A. definite integral

B. indefinite integral

C. simple integral

D. compond integral

View Answer
**Ans **: A

**Explanation**: Numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations.

Question 3

The term "numerical integration" first appears in ?

A. 1910

B. 1915

C. 1920

D. 1925

View Answer
**Ans **: B

**Explanation**: The term "numerical integration" first appears in 1915 in the publication A Course in Interpolation and Numeric Integration for the Mathematical Laboratory by David Gibb.

Question 4

______________ is a historical mathematical term that means calculating area

A. alpha

B. beta

C. quadrature

D. octature

View Answer
**Ans **: C

**Explanation**: Quadrature is a historical mathematical term that means calculating area. Quadrature problems have served as one of the main sources of mathematical analysis.

Question 5

The interpolating function may be a straight line (an affine function, i.e. a polynomial of degree 1) passing through the points. This is called the trapezoidal rule.

A. TRUE

B. FALSE

C. Can be true or false

D. Can not say

View Answer
**Ans **: A

**Explanation**: The interpolating function may be a straight line (an affine function, i.e. a polynomial of degree 1) passing through the points. This is called the trapezoidal rule.

Question 6

Bayesian Quadrature is a statistical approach to the numerical problem of computing integrals and falls under the field of probabilistic numerics.

A. TRUE

B. FALSE

C. Can be true or false

D. Can not say

View Answer
**Ans **: A

**Explanation**: Bayesian Quadrature is a statistical approach to the numerical problem of computing integrals and falls under the field of probabilistic numerics. It can provide a full handling of the uncertainty over the solution of the integral expressed as a Gaussian Process posterior variance. It is also known to provide very fast convergence rates which can be up to exponential in the number of quadrature points n.

Question 7

The stresses in the quadratic element are not ______

A. Linear

B. Uniform

C. Constant

D. Undefined

View Answer
**Ans **: C

**Explanation**: The stress applied to a material is the force per unit area applied to the material. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress. Tensile means the material is under tension. The forces acting on it are trying to stretch the material.

Question 8

For quadrilateral with 2X2 integration gives _____ sets of stress values.

A. 1

B. 2

C. 3

D. 4

View Answer
**Ans **: D

**Explanation**: The stress applied to a material is the force per unit area applied to the material. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress. Tensile means the material is under tension. The forces acting on it are trying to stretch the material.

Question 9

For degenerate four noded quadrilateral element the errors are _____

A. Constant

B. Uniform

C. Higher

D. Lesser

View Answer
**Ans **: C

**Explanation**: A degenerated element is an element whose characteristic face shape is quadrilateral, but is modeled with at least one triangular face. Degenerated elements are often used for modeling transition regions between fine and coarse meshes, or for modeling irregular and warped surfaces.

Question 10

Gauss points are also the points used for numerical evaluation of _____

A. Sureface

B. e^k

C. Elements

D. Planes

View Answer
**Ans **: B

**Explanation**: Stiffness is the rigidity of an object, the extent to which it resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is the less stiff it is. A stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.