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Definite Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals2 Marks
Question
If $\int\limits^1_0(3\text{x}^2+2\text{x}+\text{k})\text{dx}=0,$ find the value of k.
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Answer

We have,
$\int\limits^1_0(3\text{x}^2+2\text{x}+\text{k})\text{dx}=0$
$\Rightarrow\big[\text{x}^3+\text{x}^2+\text{kx}\big]^1_0=0$
$\Rightarrow1+1+\text{k}-0=0$
$\Rightarrow\text{k}=-2$

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