Yes, of course. Since you are supposed to find the area between this curve and the x axis, you will need to set up a definite integral.Jamiey1988 said:FInd the area contained by the curve and the x axis
y = (2x-7)(x+4)
Homework Equations
I don't know really where to start all I have done is multiply out the brackets like so
y = 2x^(2) + x - 28
Will the curve cross the x-axis at x = -4 and x = 7/2 ??
The concept of finding the area contained by a curve involves calculating the total space within a curve or a set of curves on a graph. This can be done by using mathematical techniques such as integration or by breaking the area into smaller, simpler shapes and adding them together.
The area contained by a curve can be calculated using various mathematical methods such as integration, which involves finding the definite integral of the curve's equation with respect to the x-axis. Other methods include using geometric formulas for specific shapes within the curve, or approximating the area using numerical methods.
Finding the area contained by a curve has many real-life applications, such as in engineering, physics, and economics. For example, engineers use this concept to calculate the area of a bridge's arch, physicists use it to determine the work done by a varying force, and economists use it to analyze demand and supply curves.
Yes, there are limitations to finding the area contained by a curve. One limitation is that the curve must have a continuous and defined equation. Another limitation is that the curve must be bounded by two points on the x-axis, otherwise the area is infinite. Additionally, the accuracy of the calculated area depends on the precision of the mathematical method used.
Yes, the area contained by a curve can be negative. This occurs when the curve intersects the x-axis at points where the function value is negative. In this case, the area below the x-axis is subtracted from the area above the x-axis, resulting in a negative value. However, in most mathematical applications, the absolute value of the area is used to represent the magnitude of the area contained by a curve.