Evaluate the Integral Using the Given Substitution A) $\frac { 27 } { 4 } \left( y ^ { 6 } + 5 y ^ { 3 } + 2 \right) ^ { 4 } + C$

question 194

Multiple Choice

Evaluate the integral using the given substitution.
- $\int 27 \left( \mathrm { y } ^ { 6 } + 5 \mathrm { y } ^ { 3 } + 2 \right) ^ { 3 } \left( 2 \mathrm { y } ^ { 5 } + 5 \mathrm { y } ^ { 2 } \right) \mathrm { dy } , \quad \mathrm { u } = \mathrm { y } ^ { 6 } + 5 \mathrm { y } ^ { 3 } + 2$

• A) \(\frac { 27 } { 4 } \left( y ^ { 6 } + 5 y ^ { 3 } + 2 \right) ^ { 4 } + C\)
• B) \(\frac { 9 } { 4 } \left( y ^ { 6 } + 5 y ^ { 3 } + 2 \right) ^ { 4 } + C\)
• C) \(27 \left( y ^ { 6 } + 5 y ^ { 3 } + 2 \right) ^ { 2 } + C\)
• D) \(\frac { 27 } { 4 } \left( y ^ { 6 } + 5 y ^ { 3 } + 2 \right) ^ { 4 } \left( 10 y ^ { 4 } + 10 y \right) + C\)

---

Definitions:

Meiosis

The process that produces sperm and ova, each of which contains only half of the parent cell’s original complement of 46 chromosomes.

Identical Twins

Twins who have developed from a single fertilized egg, sharing the same genetic makeup.

Monozygotic Twins

Identical twins that develop from a single fertilized egg, sharing the same genetics.

Dizygotic Twins

Also known as fraternal twins, are siblings that result from the fertilization of two different eggs by two different sperm cells, leading to the birth of genetically unique siblings.