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A: Explanation of the answer is as follows

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A: A detailed solution is given below

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A: The given integral,∫02fxdx+∫23fxdx

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A: Given the query is to find the length of the wire.

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A: We can find the answer as below.

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A: Given,

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A: We need to find equation of tangent

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Q: S. Find f(t), if f'(t) = df 1+ cos(2t) and f =1. %3D %3D dt

A: To find the function f(t) following the given conditions.

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A: See below the answer and explanation As per bertleby guidelines I have to solve only first question.…

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Q: 1- 2. 12 3 10 O 니 %3D 3.

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Q: So r dr do

A: Follow the procedure given below.

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A: We will use simple differentiation rules to solve this question.

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Q: Set up the definite integral required to find the area of the region between the graph of y 15- and…

A: Area between the two curves f(x) and g(x) over the integral [a,b] is given by A=∫abfx-gxdx