Xpress the integral f(x, y, z) dv e as an iterated integral in six different ways, where e is the solid bounded by the given surfaces. y = x2, z = 0, y + 3z = 9 −3 x2 f(x, y, z) dz dy dx 0 0 − y f(x, y, z) dz dx dy 0 0 0 f(x, y, z) dx dz dy − y 0 0 f(x, y, z) dx dy dz − y −3 0 f(x, y, z) dy dz dx x2 0 − 9−3z f(x, y, z) dy dx dz x2

x=4

step-by-step explanation:

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step-by-step explanation:

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a

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true