Evaluate the integral and interpret it as the area of a region. 6x + 7 - x dx 55, 55 - 32 9 9 Sketch the region. y y 8 8 6 4 2 -2 4 6 8 - 2 4 8 y y 8 8 6 6 2 -2 4 6 8 -2 4 6 8

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A: The formula for the arc length is given by: L=∫02π(x'(t))2+(y'(t))2dt Here,…

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A: b)1+1212+12+1232+.........

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: By using the formula kt=r't×r''tr't3 to find kt.rt=4 cos7t i+4 sin7t j+3t k

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A: topic - indefinite integral

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A:

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A: We can solve this as follows:

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A: Given problem:-

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A: Given f(x)=58-xwe know that the power series11-r=∑n=0∞ rn

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A: Explained below

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Q: Evaluate the integral. HINT: [Use a shortcut.] e 8x - 1 dx

A: Using substitution ,

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A: The detailed solution is given below Thank you

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A: Explained below

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