If $\int _ { 1 } ^ { 2 x } f ( t ) d t = x \sin ^ { - 1 } x$

question 237

Essay

If $\int _ { 1 } ^ { 2 x } f ( t ) d t = x \sin ^ { - 1 } x$ where f is a continuous function, find f (1).

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Definitions:

MSB Curve

A graph showing the marginal social benefit of producing one more unit of a good or service, considering both private and external benefits.

MCA Curve

MCA Curve might be a misinterpretation or uncommon term; possibly it's meant to refer to concepts like Marginal Cost (MC) in economics, which describes the change in total cost that arises when the quantity produced changes by one unit.

Marginal Social Cost

The total cost to society of producing an additional unit of a good or service, including both private costs and any externalities.

Marginal Cost

The cost added by producing one additional unit of a product or service.