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Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y=e^x, x=1, and y=1 is revolved around the line y=-2?

Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of yex x1 and y1 is revolved around the class=

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LammettHash

The fourth option is correct.

See the attached image. The red cylinder represents a washer formed by the described revolution. Its volume is

[tex]\pi((\text{outer radius})^2-(\text{inner radius})^2)(\text{height})[/tex]

so when we integrate, we take

[tex]\displaystyle\pi\int_0^1((e^x+2)^2-3^2)\,\mathrm dx[/tex]

Ver imagen LammettHash