To determine

To evaluate: ∫-11x100dx

Answer

Answer: 

∫-11x100dx= 2101

Explanation

1) Concept:

i) The Fundamental Theorem of Calculus (Part 2)

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

2) Theorem:

The Fundamental Theorem of Calculus: Suppose f is continuous on [a, b], then

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

3) Calculation:

Consider

∫-11x100dx

By using the antiderivative of each term,

∫-11x100dx=x1011011 -1

Now applying the Fundamental Theorem of Calculus (Part 2),

∫-11x100dx=1101101--1101101

By simplifying

1101--1101=2101

Conclusion:

Therefore,

∫-11x100dx= 2101