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Question
Write the coefficient a, b, c of which the value of the integral
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Solution
\[\int_{- 3}^3 \left( a x^2 + bx + c \right) d x\]
\[ = \left[ a\frac{x^3}{3} + b\frac{x^2}{2} + cx \right]_{- 3}^3 \]
\[ = 9a + \frac{9}{2}b + 3c + 9a - \frac{9}{2}b + 3c\]
\[ = 18a + 6c\]
Hence, the given integral is independent of b
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