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Definite Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDefinite Integrals2 Marks
Question
Write the coefficient a, b, c of which the value of the integral $\int\limits^3_{-3}(\text{ax}^2+\text{bx}+\text{c})\text{dx}$ is independent. 
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Answer

$\int\limits^3_{-3}(\text{ax}^2+\text{bx}+\text{c})\text{dx}$
$=\Big[\text{a}\frac{\text{x}^3}{3}+\text{b}\frac{\text{x}^2}{2}+\text{cx}\Big]^3_{-3}$
$=9\text{a}+\frac{9}{2}\text{b}+3\text{c}+9\text{a}-\frac{9}{2}\text{b}+3\text{c}$
$=18\text{a}+6\text{c}$
Hence, the given integral is independent of b.

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