Question

Integral- Volumes by Slicing and Rotation About an Axis..Volume of a Pyramid... Could you help me solving this question, please?

Answer 1

Answer: volume is 9 cubic units

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Step-by-step explanation:

Each cross section is a square with side length x, so the area of this cross section is x^2

We're integrating from x = 0 to x = 3

So we have

`\displaystyle f(x) = x^2\\\\\\\displaystyle g(x) = \int x^2 dx = (1)/(3)x^3+C\\\\\\\displaystyle \int_(a)^(b) f(x) dx = g(b) - g(a)\\\\\\\displaystyle \int_(0)^(3) x^2 dx = g(3) - g(0)\\\\\\\displaystyle \int_(0)^(3) x^2 dx = \left((1)/(3)(3)^3+C\right) - \left((1)/(3)(0)^3+C\right)\\\\\\\displaystyle \int_(0)^(3) x^2 dx = 9\\\\\\`