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If f(x) =∫x0 t sin t dt, then write the value of f '(x). - Mathematics

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If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).

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Solution

`f(x) =∫_0^x t sin t dt`
We know that integration is the inverse process of differentiation.

`∴ f ' (x) = d/dx[∫_0^xtsintdt] = x sinx`

Concept: Integration as an Inverse Process of Differentiation
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