Question

Consider the following. y - x 1 2 3 4 5 6 x - 5 -2 The xy-coordinate plane is given. A line y = x - 5, a curve y = x^2 - 5x, and a shaded region are graphed. - The line enters the window at y = -5 on the negative y-axis, goes up and right, passes through the point (1, -4) crossing the curve, crosses the x-axis at x = 5 crossing the curve, and exits the window in the first quadrant. - The curve enters the window at the origin, goes down and right becoming less steep, passes through the point (1, -4) crossing the line, changes direction at the point (2.5, -6.25), goes up and right becoming more steep, crosses the x-axis at x = 5 crossing the line, and exits the window in the first quadrant. - The area below the line and above the curve is shaded. (a) Find the points of intersection of the curves. (x, y) = (smaller x-value) (x, y) = (larger x-value) (b) Form the integral that represents the area of the shaded region. dx (c) Find the area of the shaded region. (Give an exact answer. Do not round.)

          Consider the following.
y
- x
1
2
3
4
5
6
x - 5
-2
The xy-coordinate plane is given. A line y = x - 5, a curve y = x^2 - 5x, and a shaded region are graphed.
- The line enters the window at y = -5 on the negative y-axis, goes up and right, passes through the point (1, -4) crossing the curve, crosses the x-axis at x = 5 crossing the curve, and exits the window in the first quadrant.
- The curve enters the window at the origin, goes down and right becoming less steep, passes through the point (1, -4) crossing the line, changes direction at the point (2.5, -6.25), goes up and right becoming more steep, crosses the x-axis at x = 5 crossing the line, and exits the window in the first quadrant.
- The area below the line and above the curve is shaded.
(a) Find the points of intersection of the curves.
(x, y) = (smaller x-value)
(x, y) = (larger x-value)
(b) Form the integral that represents the area of the shaded region.
dx
(c) Find the area of the shaded region. (Give an exact answer. Do not round.)

Consider the following.
y
- x
1
2
3
4
5
6
x - 5
-2
The xy-coordinate plane is given. A line y = x - 5, a curve y = x^2 - 5x, and a shaded region are graphed.
- The line enters the window at y = -5 on the negative y-axis, goes up and right, passes through the point (1, -4) crossing the curve, crosses the x-axis at x = 5 crossing the curve, and exits the window in the first quadrant.
- The curve enters the window at the origin, goes down and right becoming less steep, passes through the point (1, -4) crossing the line, changes direction at the point (2.5, -6.25), goes up and right becoming more steep, crosses the x-axis at x = 5 crossing the line, and exits the window in the first quadrant.
- The area below the line and above the curve is shaded.
(a) Find the points of intersection of the curves.
(x, y) = (smaller x-value)
(x, y) = (larger x-value)
(b) Form the integral that represents the area of the shaded region.
dx
(c) Find the area of the shaded region. (Give an exact answer. Do not round.)

Added by Aaron W.

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