#### To determine

**To evaluate:**

∫12(8x3+3x2)dx if it exists

#### Answer

37

#### Explanation

**1) Concept:**

By using fundamental theorem of calculus and rules of integration evaluate the given integral.

**2) Theorem:**

Fundamental theorem of calculus:

If f is continuous on [a, b], then ∫abfxdx=Fb-Fa.

**3) Formula:**

∫xndx=xn+1n+1+C

**3) Given:**

∫12(8x3+3x2)dx

**4) Calculation:**

Consider, ∫12(8x3+3x2)dx

Since it is continuous in the given interval, its integral exists.

By applying fundamental theorem of calculus and power rule,

∫12(8x3+3x2)dx=8x44+3x3312

=8244+3233-8144+3133

Simplify,

=32+8-2+1

=40-3

=37

**Conclusion:**

Therefore, ∫12(8x3+3x2)dx=37