Question

Find the volume of the solid whose base is the region in the xy-plane that is bounded by the parabola $y = 4 - x^2$ and the line $y = 3x$, while the top is bounded by the plane $z = x + 8$. The volume is $oxed{ }$. (Simplify your answer.)

          Find the volume of the solid whose base is the region in the xy-plane that is bounded by the parabola $y = 4 - x^2$ and the line $y = 3x$, while the top is bounded by the plane $z = x + 8$.

The volume is $oxed{ }$.
(Simplify your answer.)

Find the volume of the solid whose base is the region in the xy-plane that is bounded by the parabola y = 4 - x^2 and the line y = 3x, while the top is bounded by the plane z = x + 8.

The volume is oxed.
(Simplify your answer.)

Added by Andrea T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/17/2022

Step 1

Setting the two equations equal to each other: 4 - x^2 = 3x Rearranging the equation: x^2 + 3x - 4 = 0 Factoring the quadratic equation: (x + 4)(x - 1) = 0 Solving for x: x = -4 or x = 1 Therefore, the points of intersection are (-4, -12) and (1, 3). Show more…

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Question 9, 15.2.67 Points: 0 of 1 Save Find the volume of the solid whose base is the region in the xy-plane that is bounded by the parabola y = 4 - x^2 and the line y = 3x, while the top is bounded by the plane z = x + 8. The volume is (Simplify your answer.)