Up a Triple Integral for the Volume of the Solid $z = 14 - x ^ { 2 }$

question 100

Multiple Choice

up a triple integral for the volume of the solid bounded above by the cylinder $z = 14 - x ^ { 2 }$ and below by the paraboloid $z = x ^ { 2 } + 15 y ^ { 2 }$ .

• A)
• \( \int_{-\sqrt{7}}^{\sqrt{7}} \int_{-\sqrt{\frac{b-x^2}{a}}}^{\sqrt{\frac{b-x^2}{a}}} \int_{x^2+15y^2}^{14-x^2} d z dy d x \)
• B)
• \( \int_{-\sqrt{14}}^{\sqrt{7}} \int_{-\sqrt{\frac{b-x^2}{a}}}^{\sqrt{\frac{b-x^2}{a}}} \int_{14-x^2}^{x^2+15y^2} d z dy d x \)
• C)
• \( \int_{-\sqrt{14}}^{\sqrt{14}} \int_{-\sqrt{\frac{b-x^2}{a}}}^{\sqrt{\frac{b-x^2}{a}}} \int_{x^2+15y^2}^{14-x^2} = d z dx d y \)
• D)
• \( \int_{-\sqrt{7}}^{\sqrt{7}} \int_{-\sqrt{\frac{14-2x^2}{a}}}^{\sqrt{\frac{14-2x^2}{a}}} \int_{x^2+15y^2}^{14-x^2} = d z dy d x \)
• E)
• \( \int_{-\sqrt{7}}^{\sqrt{14}} \int_{-\sqrt{\frac{b-x^2}{a}}}^{\sqrt{\frac{b-x^2}{a}}} \int_{14-x^2}^{x^2+15y^2} = d z dy d x \)

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