   Chapter 4.3, Problem 31E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ π / 6 π / 2 csc t cot t   d t

To determine

To evaluate:

π/6π/2csctcott dt

Explanation

1) Concept:

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.

2) Calculation:

π/6π/2csctcott dt

By using the antiderivative of the function,

-csctπ/2π/6

Applying the Fundamental Theorem of Calculus,

-cscπ2--cscπ6=-csc

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