The total area under MC curve is equal to TVC
Please derive it Mathematically and Graphically using Calculus and Other Mathematical Concepts
Explain graphically and DONT just give the formula that TVC is equal to summation MC
Please give the answer and dont give any links
This is NOT covered in Study Material
I am asking for the DERIVATION of formula using Calculus, Integration and other concepts which is not given anywhere

Dear Vibhav,
The mathematical derivation of 'Area of MC = TVC' is not in the syllabus. However, to make you understand the concept let me tell you that in the short run one factor (capital) remains fixed, so any additional increase in the cost should be on the cost of employing an additional variable factor (or labour). Therefore, the sum total of all the marginal cost of producing ‘n’ units of output is called TVC of producing nth unit of output. 
Graphically, the area (shaded region) under MC curve corresponding to different output levels indicates the TVC of that output level. That is,

In case you still face other issues, feel free to ask.

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