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