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Question 3 (1 point) Find the area of the surface obtained by rotating the curve about the x-axis. $y = \frac{x^2}{4} - \frac{\ln x}{2}$, $1 \le x \le 7$ Select the correct answer. $\frac{\pi}{4} \left[ 1,720 - 81 \ln(7) - (\ln(7))^2 \right]$ $\frac{\pi}{4} \left[ 359 - 36 \ln(7) - (\ln(7))^2 \right]$ $\frac{\pi}{4} \left[ 648 - 49 \ln(7) - (\ln(7))^2 \right]$ $\frac{\pi}{4} \left[ 2,599 - 100 \ln(7) - (\ln(7))^2 \right]$

          Question 3 (1 point)
Find the area of the surface obtained by rotating the curve about the x-axis.
$y = \frac{x^2}{4} - \frac{\ln x}{2}$, $1 \le x \le 7$
Select the correct answer.
$\frac{\pi}{4} \left[ 1,720 - 81 \ln(7) - (\ln(7))^2 \right]$
$\frac{\pi}{4} \left[ 359 - 36 \ln(7) - (\ln(7))^2 \right]$
$\frac{\pi}{4} \left[ 648 - 49 \ln(7) - (\ln(7))^2 \right]$
$\frac{\pi}{4} \left[ 2,599 - 100 \ln(7) - (\ln(7))^2 \right]$

Question 3 (1 point)
Find the area of the surface obtained by rotating the curve about the x-axis.
y = (x^2)/(4) - (ln x)/(2), 1 ≤ x ≤ 7
Select the correct answer.
(π)/(4)[ 1,720 - 81 ln(7) - (ln(7))^2 ]
(π)/(4)[ 359 - 36 ln(7) - (ln(7))^2 ]
(π)/(4)[ 648 - 49 ln(7) - (ln(7))^2 ]
(π)/(4)[ 2,599 - 100 ln(7) - (ln(7))^2 ]

Added by Alvaro C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

04/10/2024

Step 1

Step 1: The formula for the surface area of a curve rotated about the x-axis is given by: $$S = 2\pi \int_{a}^{b} y \sqrt{1 + (y')^2} dx$$ Show more…

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Question 3 (1 point) Find the area of the surface obtained by rotating the curve about the x-axis. $$y = \frac{x^2}{4} - \frac{ln x}{2}, 1 \leq x \leq 7$$ Select the correct answer. $$\frac{\pi}{4}[1,720-81 ln(7)-(ln(7))^2]$$ $$\frac{\pi}{4}[359-36ln(7)-(ln(7))^2]$$ $$\frac{\pi}{4}[648-49ln(7)-(ln(7))^2]$$ $$\frac{\pi}{4}[2.599-100ln(7)-(ln(7))^2]$$