Set Up an Integral for the Length of the Curve $$y = x ^ { 4 } , 0 \leq x \leq 1$$

question 115

Multiple Choice

Set up an integral for the length of the curve.
- $$y = x ^ { 4 } , 0 \leq x \leq 1$$

• A) \(\int _ { 0 } ^ { 1 } \sqrt { 1 + 4 x ^ { 3 } } d x\)
• B) \(\int _ { 0 } ^ { 1 } \sqrt { 1 + 16 x ^ { 8 } } d x\)
• C) \(\int _ { 0 } ^ { 1 } \sqrt { 1 + 4 x ^ { 6 } } d x\)
• D) \(\int _ { 0 } ^ { 1 } \sqrt { 1 + 16 x ^ { 6 } } d x\)

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Definitions:

Depression

This condition, defined by a consistently low emotional state or a lack of enthusiasm for activities, notably hinders regular daily activities.

Downward Social Comparison

A defensive tendency to compare oneself with someone whose troubles are more serious than one’s own.

Self-verification

The process through which individuals seek to confirm their self-concept by encouraging feedback that aligns with their existing beliefs and perceptions about themselves.

Biased Affective Forecasting

The tendency for people to inaccurately predict the intensity or duration of future emotional states, often underestimating the capacity to adapt to life changes.