a) Explanation Given: The given definite integral is ∫ 0 π 2 sin θ d θ . Concept used: Integration of a function can be defined by anti derivative of that function. For any function f ( x ) = a x + C , derivative of the function can be evaluated as f ′ ( x ) = a d d x ( x ) + d d x ( C ) = a ( 1 ) + 0 = a Therefore, antiderivative of a is given by ∫ a d x = a x + C Here, a is any constant and C is integrating constant. On other hand, ∫ a d x = a ∫ d x = a x + C Formula used: Formula to evaluate the integral of the form ∫ a x n d x is shown below. ∫ a x n d x = a ∫ x n d x = a x n + 1 n + 1 + C , n ≠ − 1 Formula to evaluate the integral of the form ∫ b d x is shown below b) To determine To find: The value of the definite integral ∫ 0 π 2 sin 2 θ d θ .

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 5.5, Problem 2PS

To determine

To find: The value of the definite integral ∫0π2sinθdθ .

To determine

To find:The value of the definite integral ∫0π2sin2θdθ .

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Chapter 5.5, Problem 1PS

Chapter 5.5, Problem 3PS

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Chapter 5 Solutions

Calculus

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The value of the definite integral ∫ 0 π 2 sin θ d θ .

Solution Summary: The author explains that integration of a function can be defined by anti-derivative of that function.