Calpalned said:Homework Statement
Find the area enclosed by the curve x = t^2 -2t, y = t^0.5 and the y axis
Homework Equations
Area of a parametric curve = ∫g(t) f'(t) dt, where g(t) = y and f(t) = x
The Attempt at a Solution
I believe that the limits of integration by be found by setting x and y equal to each other and solving for y. Do I still use the given equation, or do I have to modify it as this question asks about the y-axis, not the x-axis.
Thanks
Calpalned said:I solved t^2 - 2t = x = 0 and I got t = 2 and t = 0, so those are my limits
Now, do I still use ∫g(t) f'(t) dt or do I have to modify the equation to ∫f(t) g'(t) dt ?
Integration is a mathematical concept that involves finding the area under a curve. It is used to find the exact value of an area that cannot be easily calculated using basic geometric formulas.
The two main types of integration methods used to find area are the definite integral and the indefinite integral. The definite integral calculates the area between two specific points on a curve, while the indefinite integral calculates the general area under a curve.
The Riemann sum method is a technique used to approximate the area under a curve by dividing the area into smaller, simpler shapes. This method is used as the basis for integration, where the number of smaller shapes used approaches infinity, resulting in a more accurate calculation of the area.
Yes, integration can be used to find the area of irregular shapes. By dividing the irregular shape into smaller, simpler shapes, the area can be approximated using the Riemann sum method. As the number of smaller shapes approaches infinity, the approximation becomes more accurate.
Integration is used in various fields, such as physics, engineering, and economics, to calculate real-world quantities such as displacement, work, and revenue. For example, in physics, integration is used to calculate the area under a velocity-time graph to determine the total distance traveled by an object.