f(x)

Find f(x) if

\int_{0}^{a}{f(x)dx}=\frac{6a-sin2a}{4};a>0

4 Answers

1
sadafsweetest1 ·

f(x) = 3-cos2x2

1
champ ·

How to do it ?
I need hints or solution :-(

66
kaymant ·

Differentiate both sides w.r.t. the upper limit a:
f(a)=\dfrac{\mathrm d}{\mathrm da}\int_0^af(x)\ \mathrm dx=\dfrac{6-2\cos2a}{4}

1
champ ·

Thank you :-)

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