Hi,
I don't have any question specifically but I'm very confused on this.
In integration to find area under/above a curve, when do you integrate:
1) with respect to y
2) with respect to x
3) using x coordinates
4) using y coordinates
Thanks for your help! :)
Look at the piecemeal unit of dArea you are integrating. Is is some y dx or xdy? It is those little differential areas you are integrating.
Here is a x dy dArea.
http://education.yahoo.com/homework_help/math_help/solutionimages/minicalcgt/6/1/1/minicalcgt_6_1_1_3_50/f-413-21.gif
Thanks ^^
Hi there! I'd be happy to help you understand when to integrate with respect to y or x, and when to use x or y coordinates when finding the area under/above a curve.
1) Integrating with respect to y:
When integrating with respect to y, you are finding the area between the curve and the y-axis. In this case, you want to express the equation of the curve in terms of y. You integrate from the lowest value of y to the highest value of y to find the total area.
2) Integrating with respect to x:
When integrating with respect to x, you are finding the area between the curve and the x-axis. In this case, you want to express the equation of the curve in terms of x. You integrate from the lowest value of x to the highest value of x to find the total area.
3) Using x coordinates:
Using x coordinates means you are finding the area between the curve and the vertical lines that define a specific interval on the x-axis. You need to identify the x-values that bound the area you want to find, and then integrate the equation with respect to y within those x-boundaries.
4) Using y coordinates:
Using y coordinates means you are finding the area between the curve and the horizontal lines that define a specific interval on the y-axis. You need to identify the y-values that bound the area you want to find, and then integrate the equation with respect to x within those y-boundaries.
In summary, whether you integrate with respect to y or x and whether you use x or y coordinates depends on which axis (x or y) you want to measure the area with respect to and the boundaries you want to define for that area.
I hope this explanation clears up your confusion! Let me know if you have any further questions.