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Question
\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.
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Solution
\[\text{We have}, \]
\[ \int_0^a 3 x^2 d x = 8\]
\[ \Rightarrow \left[ 3 \frac{x^3}{3} \right]_0^a = 8\]
\[ \Rightarrow a^3 = 8\]
\[ \Rightarrow a = 2\]
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