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Question
If \[\int\limits_0^a 3 x^2 dx = 8,\] write the value of a.
Solution
\[\text{We have}, \]
\[ \int_0^a 3 x^2 d x = 8\]
\[ \Rightarrow \left[ 3\frac{x^3}{3} \right]_0^a = 8\]
\[ \Rightarrow \left[ x^3 \right]_0^a = 8\]
\[ \Rightarrow a^3 - 0 = 8\]
\[ \Rightarrow a = \sqrt[3]{8}\]
\[ = 2\]
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