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Question
If \[\int\limits_0^1 \left( 3 x^2 + 2x + k \right) dx = 0,\] find the value of k.
Solution
\[\text{We have}, \]
\[ \int_0^1 \left( 3 x^2 + 2x + k \right) d x = 0\]
\[ \Rightarrow \left[ x^3 + x^2 + kx \right]_0^1 = 0\]
\[ \Rightarrow 1 + 1 + k - 0 = 0\]
\[ \Rightarrow k = - 2\]
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