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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
Question
$\text{If} \int\limits_0^{1} (3x^{2} + 2x + k) dx = 0$ find the value of k.
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Answer

$\text{If} \int\limits_0^{1} (3x^{2} + 2x + k) dx = 0$$\Rightarrow \bigg[\frac{3x^{3}}{3} + \frac{2x^{2}}{2} + kx\bigg]^{1}_{0} = 0$
$\Rightarrow 1 + 1 + k = 0 \Rightarrow k = -2$

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