#### To determine

**To evaluate: **

∫12v5+3v6v4 dv

#### Answer

**Answer: **

∫12v5+3v6v4 dv=172

#### Explanation

**1) Concept:**

i) The Fundamental Theorem of Calculus (part 2): Suppose f is continuous on [a, b], then

∫abfxdx=Fb-F(a), where F is antiderivative of f, that is F'=f.

ii) Separate out the integration and then use antiderivative of each term

**2) Calculation: **

∫12v5+3v6v4 dv

After separating the denominator, the above integration becomes

∫12( v5v4+ 3v6v4 ) dv

By separating the integration

∫12v dv+∫123v2dv

By using the antiderivative,

v222 1+3v3321

Applying the Fundamental Theorem of Calculus,

222-12+3[233-133]

By simplifying,

2-12+(8-1)

After simplifying the above expression,

32+7=172

**Conclusion:**

Therefore,

∫12v5+3v6v4 dv=172