Explanation Given information: The area function is denoted by A ( x ) and the lower limit of the A ( x ) is given as a = 0 . f ( x ) = x 2 − sin x Formula used: The fundamental theorem of calculus part (II). The area function is given by, A ( x ) = ∫ a x f ( t ) d t where f is continuous on an interval I and a is a point on I . The derivative of the area function is, A ' ( x ) = d d x ∫ a x f ( x ) d x = f ( x ) The sum rule for indefinite integrals, ∫ ( f ( x ) + g ( x ) ) d x = ∫ f ( x ) d x + ∫ g ( x ) d x The power rule of indefinite integrals. ∫ x n d x = x n + 1 n + 1 + C when n ≠ ( − 1 ) Calculation: By the fundamental theorem of calculus part (II), we can integrate the function f ( x ) to obtain the area function. A ( x ) = ∫ 0 x f ( t ) d t = ∫ 0 x t 2 − sin t d t = ∫ 0 x t 2 d t −

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 5.5, Problem 5E

To determine

To find: The antiderivative of f(x)=x2−sinx to obtain he area function and the derivative of the area function.Also show that derivative of area function is equals to f(x) .

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Chapter 5.5, Problem 4E

Chapter 5.5, Problem 6E

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The antiderivative of f ( x ) = x 2 − sin x to obtain he area function and the derivative of the area function.Also show that derivative of area function is equals to f ( x ) .

Solution Summary: The author explains the area function and its derivative, which is equal to f(x).

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To find: The antiderivative of f(x)=x2−sinx to obtain he area function and the derivative of the area function.Also show that derivative of area function is equals to f(x) .

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Chapter 5 Solutions