Can someone please show me the steps to this problem...Thanks in advance.
Let f(x) = Ð9xÐ. For the area above the x-axis and between the lines x= -9 and x=18
a. draw and label a sketch with
the area shaded
b. find the area of the region in
the xy-plane under the graph
of f(x)
describe in words what Ð9xÐ is supposed to be.
On my Mac it came out weird.
Sorry it came out that way:
Let f(x) =|9x|. For the area above the x-axis and between the lines x= -9 and x=18
Reiny this is the complete problem...Sorry about all that...Thank you
Let f(x) =|9x|. For the area above the x-axis and between the lines x= -9 and x=18
a. draw and label a sketch with
the area shaded
b. find the area of the region in
the xy-plane under the graph
of f(x)
Can anyone help with the following problem please...Thank u so much
Let f(x) =|9x|. For the area above the x-axis and between the lines x= -9 and x=18
a. draw and label a sketch with
the area shaded
b. find the area of the region in
the xy-plane under the graph
of f(x)
To solve this problem, follow these steps:
a. Sketch the graph:
- Draw the x-axis and y-axis on a piece of graph paper.
- Locate the points (-9, 0) and (18, 0) on the x-axis.
- Plot these points and draw a line connecting them. This line represents the x-axis.
- Now, consider the equation of the function f(x) = Ð9xÐ. To plot this graph, you would need to substitute different values for x to get corresponding y-values.
- Choose a few values for x, such as -9, -6, -3, 0, 3, 6, 9, 12, 15, and 18. Calculate the corresponding y-values by substituting each value of x into the equation f(x) = Ð9xÐ.
- Plot the points (x, f(x)) on the graph. Connect the points to form a curve that represents the graph of f(x).
- Finally, identify the region above the x-axis and between the lines x = -9 and x = 18. Shade this region on your graph.
b. Find the area of the shaded region:
- To find the area under the graph of f(x), we need to calculate the definite integral of f(x) between the limits of x = -9 and x = 18.
- The integral of f(x) with respect to x can be represented by ∫(from -9 to 18) f(x) dx.
- Substitute the equation of f(x) = Ð9xÐ into the integral: ∫(from -9 to 18) Ð9xÐ dx.
- Integrate this function using the rules of integration. The integral symbol represents the area under the graph, so the result of the integration will be the area of the shaded region.
- Calculate the definite integral and determine the area of the shaded region.
Following these steps will help you sketch the graph, shade the region, and find the area under the graph of the given function f(x).