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The area of the region enclosed by the graph of y 2 x2 1 and the line y 2 x 5 is what?
∣∣2−1 . -6 + 15 = 9 To calculate the area between the curves y = 2 x2 + 1 and y = 2 x + 5, we must evaluate the integral ∫ab(2x+5)−(2x2+1)dx . To determine which values to use for a and b as the limits of the integral, we calculate the x values where the two curves intersect. Solve 2 x2 + 1 = 2 x + 5 by factoring to get x = 2 and x = -1. Set a = -1, b = 2. The enclosed area, A , is therefore given by the equation A=∫2−1(2x+5)−(2x2+1)dx=∫2−1−2x2+2x+2x+4 dx=[−2x33+x2+4x]
What else can I help you with?
How do you graph X - Y is less than or equal to 0?
You draw the line X - Y = 0 or, equivalently, X = Y. Since points on the line are included in the desired region, the line should be solid. Then the required region is the area of the line and all points above it.
How do you graph x is greater than or equal to y?
Take a blank graph with 'x' and 'y' axes on it. Draw a 45-degree line on the graph. The line goes through the origin, and from the origin, it goes down-left and up-right. The slope of the line is 1, and its equation is y=x. The region "y is greater than or equal to x" is every point on that line, plus every point on the side above it (to the left of it).
Is the first derivative of a function is a constant then its graph is?
A line. The derivative of a function is its slope. If the slope is a constant then the graph is a line.
What is the steepness on a line graph called?
The steepness of a line graph is called the "gradient" ------------------------------- or slope.
How can you tell by looking at a graph its a function?
Draw a graph of a given curve in the xoy plane. Now draw a vertical line so that it cuts the graph. If the vertical line cuts the graph in more than one ordinate then given graph is not a function. If it cuts the graph at a single ordinate such a graph is a function.(is called vertical line test)
Area enclosed by a line?
In the subject art an area enclosed by a line is a shape.
How would you know that the boundary line is enclosed in a graph?
The boundary line is solid. If not it will be a dashed line.
Which inequality symbols are represented by a solid line on a graph?
The graph of an inequality is a region, not a line.
What is similar to a line graph?
An area graph. It fills the area between a line and the line below or the x-axis.
How do you graph y is greater than 2x?
First draw a dashed line for y = 2x and then highlight the are above the line. You can highlight the area by shading it and state that the shaded area is the region of interest, or (my preference) shading the area below the line and state that the unshaded area is the region of interest. The advantages of the second option become clearer when you have several inequalities defining a region.
Which type of graph is best suited for graphing the temperature of an area?
line graph!
How do you graph X - Y is less than or equal to 0?
You draw the line X - Y = 0 or, equivalently, X = Y. Since points on the line are included in the desired region, the line should be solid. Then the required region is the area of the line and all points above it.
What does the area under the a speed time graph represent?
In a speed - time graph, the area under the line equals the distance traveled during the time interval A of ____ = L X W A of triangle = 1/2 bh
How do you graph y greater than -x?
The graph of y > - x is an area, firstly draw the line y = -x which is a line sloping diagonally upwards to the left at 45o and the area where y > -x is the area above the line
How do you multiply and divide on a line graph?
line graph x line graph = divided line graph
Is the region enclosed by a circle convex?
No, the region enclosed by a circle is not considered convex because it contains points within the circle that do not lie on the boundary of the circle. In convex regions, any line segment connecting two points inside the region will also lie completely inside the region.
In the graph of a linear inequality the shaded region above or below the line is called?
The shaded region above or below the line in the graph of a linear inequality is called the solution region. This region represents all the possible values that satisfy the inequality. Points within the shaded region are solutions to the inequality, while points outside the shaded region are not solutions.
