Evaluate the Integral $\int _ { 0 } ^ { 1 } \frac { x ^ { 2 } } { \left( 5 + 3 x ^ { 3 } \right) ^ { 2 } }$

question 43

Multiple Choice

Evaluate the integral.
- $\int _ { 0 } ^ { 1 } \frac { x ^ { 2 } } { \left( 5 + 3 x ^ { 3 } \right) ^ { 2 } }$ dx

• A) \(\frac { 43 } { 3 }\)
• B) \(\frac { 1 } { 120 }\)
• C) \(\frac { 13 } { 6 }\)
• D) \(\frac { 27 } { 40 }\)

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Definitions:

Negligence

The failure to exercise the care that a reasonably prudent person would exercise in similar circumstances, resulting in harm or damage.

Design Defect

A flaw in the planning or design of a product that makes it inherently unsafe or faulty.

Alternative Design

A different approach or solution, often proposed to address flaws in an original design concept.

Market-Share Liability

A legal theory holding manufacturers proportionately liable for damages based on their market share of a harmful product.