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Calculus2.1

# Calculus2.1 - Section 6.2 Volume Consider a solid whose...

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Section 6.2: Volume

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Consider a solid whose base is the region bounded by y=1-x, y=2x+5, x=0 and x=3. If the cross sections are squares, set up an integral to find volume Volume of box = height * width * length This isn't a box, but we could break in into pieces, pretend they are boxes, then take limit. length = (2x+5) - (1-x) height = (2x+5) - (1-x) since cross sections are squares width = x
      2 ** 1 2 5 1 n k k k k Volume x x x       3 2 0 2 5 1 237 Volume x x dx : What if cross sections are circles?? Eg   2 2 5 (1 ) 2 xx x      2 3 0 2 5 ) 2 dx

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2 Consider region bounded by y=x and y=2x Find volume when rotated about:   2 2 2 (2 ) ( ) x x x   2 22 0 (2 ) ( ) x x dx (using was x- h axis ers) If we slice perpendicular to x-axis, we get a washer Thickness= x
  22 (2 3) ( x x x  2 0 ( x x dx y = -3 Important: The axis is the center of the washer

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Calculus2.1 - Section 6.2 Volume Consider a solid whose...

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