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    Would somebody also know how integration can find the area under a curve. I understand how the gradient lets say of a function f(x) affects the area underneath. Isn't it also that f '(x) is the rate of change of y with respect to x. ( it is the gradient of the curvy function)... So therefore f'(x), the gradient, must have to be related to the area somehow. I understand how to do the calculations, it's merely understanding how the method finds it. Any help would be very appreciated plus rep.
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    Somebody please help me!!!!
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    (Original post by MathMeister)
    Would somebody also know how integration can find the area under a curve. I understand how the gradient lets say of a function f(x) affects the area underneath. Isn't it also that f '(x) is the rate of change of y with respect to x. ( it is the gradient of the curvy function)... So therefore f'(x), the gradient, must have to be related to the area somehow. I understand how to do the calculations, it's merely understanding how the method finds it. Any help would be very appreciated plus rep.
    Take a look at this post
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    Has anybody anything else to help understand? Rep btw
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    Has anybody anything else to help understand? Rep btw
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    (Original post by MathMeister)
    Has anybody anything else to help understand? Rep btw
    atsruser has already linked you to one explanation.

    You can also look up the Fundamental Theorem of Calculus which provides a proof of why the process of integration (i.e. reversing differentiation) gives you the area under a curve, but to understand it fully you need some pre-requisites from a university course!

    It's good that you're asking questions, but don't try to get ahead of yourself at this stage - concentrate on understanding the "mechanics" of the process so that you can do the basic manipulation first. Understanding can come later once you are fluent with the techniques.
 
 
 
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