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If $\int_{-3}^{2} \mathrm{f}(\mathrm{x}) \mathrm{dx}=\frac{7}{3}$ and $\int_{-3}^{9} \mathrm{f}(\mathrm{x}) \mathrm{dx}=-\frac{5}{6}$, then what is the
value of $\int_{2}^{9} \mathrm{f}(\mathrm{x}) \mathrm{dx}$ ?
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value of $\int_{2}^{9} \mathrm{f}(\mathrm{x}) \mathrm{dx}$ ?
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Verified Answer
The correct answer is:
$-\frac{19}{6}$
Value of the integral $\int_{2}^{9} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}$
$=\int_{-3}^{9} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}-\int_{-3}^{2} \mathrm{f}(\mathrm{x}) \mathrm{dx}$
Given, $\int_{-3}^{9} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=\frac{-5}{6}$ and $\int_{-3}^{2} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=\frac{7}{3}$
Putting these values in equation (i)
$\int_{2}^{9} f(x) d x=\frac{-5}{6}-\frac{7}{3}=-\frac{19}{6}$
$=\int_{-3}^{9} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}-\int_{-3}^{2} \mathrm{f}(\mathrm{x}) \mathrm{dx}$
Given, $\int_{-3}^{9} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=\frac{-5}{6}$ and $\int_{-3}^{2} \mathrm{f}(\mathrm{x}) \mathrm{d} \mathrm{x}=\frac{7}{3}$
Putting these values in equation (i)
$\int_{2}^{9} f(x) d x=\frac{-5}{6}-\frac{7}{3}=-\frac{19}{6}$
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