13 Exercises 6.1: Volumes by the Washer Method إيجاد حجوم المجسمات

Volumes by the Washer Method
In Exercises 45–48, find the volume of the solid generated by revolving each region about the y-axis:
45. The region enclosed by the triangle with vertices (1, 0), (2, 1), and (1, 1)
46. The region enclosed by the triangle with vertices (0, 1), (1, 0), and (1, 1)
47. The region in the first quadrant bounded above by the parabola y = x^2
, below by the x-axis, and on the right by the line x = 2
48. The region in the first quadrant bounded on the left by the circle x^2 + y^2 = 3, on the right by the line x = square root of 3, and above by the line y = square root of 3

In Exercises 49 and 50, find the volume of the solid generated by
revolving each region about the given axis.
49. The region in the first quadrant bounded above by the curve y = x^2
, below by the x-axis, and on the right by the line x = 1, about the line x = -1

50. The region in the second quadrant bounded above by the curve y = -x^3
, below by the x-axis, and on the left by the line x = -1, about the line x = -2

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