Use a fiNite Sum to Estimate the Average Value of the Function

question 272

Multiple Choice

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.
- $\mathrm { f } ( \mathrm { t } ) = 3 + \sin \pi \mathrm { t }$ on $[ 0,2 ]$ divided into 4 subintervals

• A) \(\frac { 6 + \sqrt { 2 } } { 2 }\)
• B) \(\frac { 12 + \sqrt { 2 } } { 4 }\)
• C) 3
• D) 0

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Definitions:

Knee

A hinge joint that connects the thigh bone (femur) to the shin bone (tibia).

Shoulder

The region of the body where the upper arm bone (humerus), shoulder blade (scapula), and collarbone (clavicle) meet.

Diarthrosis

A type of joint that allows for free movement between the bones it connects, commonly known as a synovial joint.

Amphiarthrosis

A type of joint that is slightly movable, providing a balance between mobility and stability, found in the vertebral column.