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uestion 23 he region enclosed by the graphs of \( y=x^{2} \) and \( y=2 x \) is the base of a solid. For the solid, each cross section perpendicular to the \( y \)-axis mes its base in the xyplane. Which of the following expressions gives the volume of the solid? (A) \( \quad 3 \int_{0}^{4}\left(\sqrt{y}-\frac{y}{2}\right)^{2} d y \) (B) \( \quad 3 \int_{0}^{4}\left(\sqrt{y}+\frac{y}{2}\right)^{2} d y \) C \( 3 \int_{0}^{2}\left(2 x-x^{2}\right)^{2} d x \) (D) \( 3 \int_{0}^{2}\left(2 x+x^{2}\right)^{2} d x \)

          uestion 23
he region enclosed by the graphs of \( y=x^{2} \) and \( y=2 x \) is the base of a solid. For the solid, each cross section perpendicular to the \( y \)-axis mes its base in the xyplane. Which of the following expressions gives the volume of the solid?
(A) \( \quad 3 \int_{0}^{4}\left(\sqrt{y}-\frac{y}{2}\right)^{2} d y \)
(B) \( \quad 3 \int_{0}^{4}\left(\sqrt{y}+\frac{y}{2}\right)^{2} d y \)

C \( 3 \int_{0}^{2}\left(2 x-x^{2}\right)^{2} d x \)
(D) \( 3 \int_{0}^{2}\left(2 x+x^{2}\right)^{2} d x \)

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uestion 23
he region enclosed by the graphs of y=x^2 and y=2 x is the base of a solid. For the solid, each cross section perpendicular to the y-axis mes its base in the xyplane. Which of the following expressions gives the volume of the solid?
(A) 3 ∫0^4(√(y)-(y)/(2))^2 d y
(B) 3 ∫0^4(√(y)+(y)/(2))^2 d y

C 3 ∫0^2(2 x-x^2)^2 d x
(D) 3 ∫0^2(2 x+x^2)^2 d x

Added by Juan Francisco W.

Calculus: Early Transcendental Functions

Robert T. Smith, Roland B. Minton 3rd Edition

Chapter 5

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Solved by Expert Vishal Parmar

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The problem involves finding the volume of a solid whose base is enclosed by the graphs of \(y = x^2\) and \(y = 2x\). The cross sections of the solid perpendicular to the \(y\)-axis are squares, as implied by the square of the difference of the functions in the Show more…

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uestion 23 he region enclosed by the graphs of \( y=x^{2} \) and \( y=2 x \) is the base of a solid. For the solid, each cross section perpendicular to the \( y \)-axis mes its base in the xyplane. Which of the following expressions gives the volume of the solid? (A) \( \quad 3 \int_{0}^{4}\left(\sqrt{y}-\frac{y}{2}\right)^{2} d y \) (B) \( \quad 3 \int_{0}^{4}\left(\sqrt{y}+\frac{y}{2}\right)^{2} d y \) C \( 3 \int_{0}^{2}\left(2 x-x^{2}\right)^{2} d x \) (D) \( 3 \int_{0}^{2}\left(2 x+x^{2}\right)^{2} d x \)

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