Answer:
We have, \[\int_{0}^{1}{(3{{x}^{2}}+2x+K)dx=0}\] \[\Rightarrow \] \[[{{x}^{3}}+{{x}^{2}}+Kx]_{0}^{1}=0\] \[\Rightarrow \] \[(1+1+K)-0=0\] \[\Rightarrow \] \[K=-\,2\]
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