Evaluate the Integral $$\int _ { 1 } ^ { 2 } ( ( 2 - 7 t ) \mathbf { i } + 5 \sqrt { t } \mathbf { j } ) d t$$

question 8

Multiple Choice

Evaluate the integral.
- $$\int _ { 1 } ^ { 2 } ( ( 2 - 7 t ) \mathbf { i } + 5 \sqrt { t } \mathbf { j } ) d t$$

• A) \(- \frac { 17 } { 2 } + \frac { 10 } { 3 } ( 2 \sqrt { 2 } - 1 )\)
• B) \(- \frac { 23 } { 2 } \mathbf { i } + \frac { 10 } { 3 } ( 2 \sqrt { 2 } - 1 ) \mathbf { j }\)
• C) \(- \frac { 17 } { 2 } \mathbf { i } + \frac { 10 } { 3 } ( 2 \sqrt { 2 } - 1 ) \mathbf { j }\)
• D) \(5 \frac { \sqrt { 2 } - 2 } { 4 } \mathbf { j }\)

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Definitions:

AVC

The average variable cost is calculated by dividing the total variable costs by the produced output quantity.

Marginal Revenue

The increase in revenue that results from the sale of one additional unit of output.

Average Variable Cost

The total variable costs divided by the quantity of output produced, representing the variable cost per unit.

Average Total Cost

The total cost of production divided by the quantity of output produced, encompassing both fixed and variable costs.