Math Problem Statement
Determine whether the following integrals are improper or not and state the reason of your answer.
Then evaluate the following integrals :
(a) ( \int_{0}^{\frac{\pi}{4}} 10 \sin (2 t) \cos (2 t) \sqrt{\cos ^{2}(2 t)+5} d t )
Solution
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Math Problem Analysis
Mathematical Concepts
Definite Integrals
Improper Integrals
Trigonometric Functions
Integration Techniques
Formulas
\( \sin(2t) \cos(2t) = \frac{1}{2} \sin(4t) \)
Theorems
Trigonometric Identity
Improper Integral Conditions
Suitable Grade Level
Undergraduate
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