Integrals

[meg764]

Can someone please explain this problem to me: I have to use integrals to find volumes with known cross sections but i just don't understand. Thanks!

Consider a solid bounded by y=2ln(x) and y=0.9((x-1)^3) in the first quadrant. If cross sections taken perpendicular to the x-axis are isosceles right triangles with the hypotenuse in the base, find the volume of this solid.

 

[Deleted member 4993]

Can someone please explain this problem to me: I have to use integrals to find volumes with known cross sections but i just don't understand. Thanks!

Consider a solid bounded by y=2ln(x) and y=0.9((x-1)^3) in the first quadrant. If cross sections taken perpendicular to the x-axis are isosceles right triangles with the hypotenuse in the base, find the volume of this solid.

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[BigGlenntheHeavy]

\(\displaystyle V \ = \ \frac{1}{4}\int_{1}^{2.207}[2ln|x|-.9(x-1)^{3}]^{2}dx \ = \ .090687 \ cu. \ units\)

\(\displaystyle Above \ is \ perpendicular \ to \ x \ axis.\)

\(\displaystyle V \ = \ \frac{1}{4}\int_{0}^{1.583}\bigg[(\frac{y}{.9})^{1/3}+1-e^{y/2}\bigg]^{2}dy \ = \ .06696 \ cu. \ units\)

\(\displaystyle Above \ is \ perpendicular \ to \ y \ axis, \ see \ graph \ below.\)

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