Use Part 1 of the Fundamental Theorem of Calculus to Find

question 45

Multiple Choice

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. $$h ( x ) = \int _ { 1 } ^ { \sqrt { x } } \frac { z ^ { 2 } } { z ^ { 4 } + 1 } d z$$

• A) \(\frac { \sqrt { x + 1 } } { x ^ { 2 } + 2 }\)
• B) \(\frac { \sqrt { x ^ { 2 } + 1 } } { 2 }\)
• C)
• \(\frac { \sqrt { x } } { 2 \left( x ^ { 2 } + 1 \right) }\)
• D) \(\frac { \sqrt { x } } { x ^ { 2 } + 1 }\)
• E) none of these

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Definitions:

Pretest

An assessment given before a main intervention or treatment to establish a baseline measure of the participants' knowledge or skills.

Experimental Manipulation

The deliberate alteration of variables in an experimental setup to study its effects on the outcome.

Participant's Behavior

The actions or reactions of individuals taking part in a study, influenced by experimental conditions or their own characteristics.

Internal Validity

The extent to which an experiment is free from outside variables that might affect the results, ensuring that the outcome is a true reflection of the experimental variables.