Evaluate the Integral Using Integration by Parts $\int x ^ { 2 }$

question 95

Multiple Choice

Evaluate the integral using integration by parts.
- $\int x ^ { 2 }$ $\mathrm { e } ^ { 2 x }$ dx

• A) \(\mathrm { e } ^ { 2 x }\) \(\left( \frac { x ^ { 2 } - x } { 2 } \right)\) + 1 + C
• B) \(\mathrm { e } ^ { 2 x }\) \(\left( \frac { x ^ { 2 } - 4 x } { 2 } \right)\) + C
• C) \(\mathrm { e } ^ { 2 x }\) \(\left( \frac { x ^ { 2 } - 2 x } { 2 } \right)\) + C
• D) \(\mathrm { e } ^ { 2 x }\) \(\left( \frac { 2 x ^ { 2 } - 2 x + 1 } { 4 } \right)\) + C

Differentiate between aptitude and achievement tests.

Grasp the importance and implications of subtest scores in identifying specific learning disabilities.

Understand the significance of a normal distribution in the context of intelligence scores.

Recognize the role of personality factors in influencing success among individuals with high intelligence.

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Definitions:

Straightness

The measure of how closely a line or feature aligns with a true straight line, often evaluated to ensure precision in manufactured parts.

Circularity

The degree to which a form or surface approaches a perfect circle, often a crucial factor in precision engineering.

Angularity

A condition of having a specified angle or orientation in relation to a datum or reference plane, used in precision manufacturing and machining.

Circularity

A geometric tolerance that limits the amount of variation from a perfect circle, often applied to cylindrical parts to ensure they rotate or fit smoothly.