Theory-Based MCQs on Integration

Integration is used in geometry to find:

• Derivatives

• Areas and volumes

• Limits

• Angles

The centroid of a plane region is defined as:

• Midpoint of the base

• Geometric center of mass

• Highest point

• Farthest point from origin

The method used to find volume by rotating a region about an axis is called:

• Shell method

• Rotation method

• Revolution method

• Disk or washer method

The Trapezoidal Rule is used for:

• Solving equations

• Approximating definite integrals

• Finding derivatives

• Drawing curves

The shape of the region considered in the Trapezoidal Rule is:

• Triangle

• Circle

• Trapezoid

• Rectangle

Simpson's Rule approximates the function by using:

• Rectangles

• Tangents

• Straight lines

• Parabolas

Simpson's Rule provides better accuracy when the function is:

• Linear

• Piecewise constant

• Smooth and continuous

• Discontinuous

The area under a curve in Cartesian coordinates is evaluated using:

• Derivatives

• Algebraic rules

• Definite integrals

• Limits

The area enclosed by a polar curve is found using integration with respect to:

• x

• y

• r

• θ

In polar coordinates, area is calculated using:

• Triangular sectors

• Circular segments

• Radial strips

• Sectors of a circle