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