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The integral expression is .
Consider .
Assume .
Apply derivative on each side.
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Change of integral limits:
Lower limit: If then .
Upper limit: If then .
Substitute , and change of limits in .
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Property of definite integral: .
Replace the variable with .
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Hence it is verified.
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Graphically verify the above expression.
Consider an example function .
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Consider the lower and upper limits as and .
Here we need to prove,.
Graphically the areas of the regions under the curve are same and the value is .
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