If ^ a _03x^2 dx=8, Write the value of a. - Vidyadip

Question

If $\int\limits^{\text{a}}_03\text{x}^2\text{ dx}=8,$ Write the value of a.

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Answer

We have,
$\int\limits^{\text{a}}_03\text{x}^2\text{ dx}=8$
$\Rightarrow\Big[3\frac{\text{x}^3}{3}\Big]^{\text{a}}_0=8$
$\Rightarrow\big[\text{x}^3\big]^{\text{a}}_0=8$
$\Rightarrow\text{a}^3-0=8$
$\Rightarrow\text{a}=\sqrt[3]{8}$
$\Rightarrow\text{a}=2$

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