To determine
To evaluate:
∫-55π dx
Answer
∫-55π dx=10π
Explanation
1) Concept:
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.
2) Calculations:
∫-55π dx
Taking constant outside the integral,
∫-55π dx= π∫-551·dx
By using the antiderivative and applying the Fundamental Theorem of Calculus,
π∫-551·dx =πx5-5
=π5--5=10π
Conclusion:
Therefore,
∫-55π dx=10π