Question

Find the arc length of the part of the curve f(x) = e^{2x}, from x = 0 and x = 3. Use your calculator and round to the hundredths place. Find the arc length of the part of the curve f(x) = sin(x^2), from x = 0 and x = ?. Use your calculator and round to the hundredths place.

          Find the arc length of the part of the curve f(x) = e^{2x}, from x = 0 and x = 3.
Use your calculator and round to the hundredths place.

Find the arc length of the part of the curve f(x) = sin(x^2), from x = 0 and x = ?.
Use your calculator and round to the hundredths place.
        
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Find the arc length of the part of the curve f(x) = e^2x, from x = 0 and x = 3.
Use your calculator and round to the hundredths place.

Find the arc length of the part of the curve f(x) = sin(x^2), from x = 0 and x = ?.
Use your calculator and round to the hundredths place.

Added by David R.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Find the arc length of the part of the curve f(x) = e^{2x}, from x = 0 and x = 3. Use your calculator and round to the hundredths place. Find the arc length of the part of the curve f(x) = sin(x^2), from x = 0 and x = ̀π. Use your calculator and round to the hundredths place.
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Transcript

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00:01 In this question, we are asked to write down the formulas for the arc length of the given functions, and then use a calculator to calculate the integrals.
00:11 So the arc length equals, in the first case to the integral from 0 to 3, of the square root of 1 plus f prime of x squared d x, where f prime of x is the derivative of the function f and equals to 2 times e to the 2x, and that means that f prime squared of x equals to 4 times e to the 4x and then the arc length equals to the integral from 0 to 3 of the square root of 1 plus 4 times e to the 4x dx.
01:00 To calculate this integral i will use wolfram alpha so we will ask it to integrate the square root of 1 plus 1 plus 4 times e to the 4x from 0 to 3.
01:36 So yeah, i think that's what we're asked to calculate and the integral approximately equals to 402 .55.
01:49 Alright, that's the value, the arc length of the first curve.
01:53 Now let's move on to the next one.
01:56 It's the arc length of sine x squared from 0 to pi.
02:01 The formula is l equals to the integral from 0 to pi...
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