What does integration wrt to a different function other than x mean graphically? for instance ∫x²dx within certain limits (say a and b) is area under the curve and the x axis in between those limits. So does integrating wrt to, say sinx, is area under the function and sinx? eg ∫sin²x d(sinx) in limits a and b - is that the area btw sin²x and sinx in these limits? If yes then how exactly? in the usual cartesian plane with x and y as both the axes? Or maybe like on a new distorted kinda cartesian plane with sinx as x axis which makes -sinx as the y axis (as sinx is straightened to x hence the place distorts to form -sinx on y axis?) and then here sin²x would i guess look the same as x² curve and hence has the same area? What does ∫sin²x d(sinx) even signify (without reducing d(sinx) to sinx)?
2026-04-09 05:47:25.1775713645
Graphical interpretation of integration with respect to a certain function
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