Consider the region R in the first quadrant, bound by the graphs of y = 3x^2, y = 4 - x and x = 0. Set up the integral that calculates the volume of the region R that is rotated about the line y = 5.
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To do this, we set them equal to each other: 3x^2 = 4 - x Rearrange the equation: 3x^2 + x - 4 = 0 Now, we can find the roots of this quadratic equation. Since we are only interested in the first quadrant, we only need the positive root. We can use the Show more…
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