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CBSE Class 12 · 2014 · Definite IntegralsVery Short Answer

If

f (x) = \int_{0}^{x} t sin t d t

, then write the value of

f^{'} (x)

.

Answer: $x sin x$

Solution

By the Fundamental Theorem of Calculus, if

f (x) = \int_{0}^{x} g (t) d t

then

f^{'} (x) = g (x)

. Here

g (t) = t sin t

, so

f^{'} (x) = x sin x .

f^{'} (x) = x sin x

CBSE Class 12 Board · 2014 · Subjective

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