If _-3^2 f(x) dx = 7/3 and _-3^9 f(x) dx = -5/6 , then what is the value of _2^9 f(x) dx ? - Mathematics MCQ Mathematics Mock Test - 8 2026 | ExamTest.live

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If \int_{- 3}^{2} f (x) d x = \frac{7}{3} and \int_{- 3}^{9} f (x) d x = - \frac{5}{6}, then what is the value of \int_{2}^{9} f (x) d x ?

Solution & Step-by-step Explanation

Using the property of definite integrals: \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x Let a = - 3, b = 2, c = 9 . \int_{- 3}^{9} f (x) d x = \int_{- 3}^{2} f (x) d x + \int_{2}^{9} f (x) d x Substitute the given values: - \frac{5}{6} = \frac{7}{3} + \int_{2}^{9} f (x) d x \int_{2}^{9} f (x) d x = - \frac{5}{6} - \frac{7}{3} = - \frac{5}{6} - \frac{14}{6} = - \frac{19}{6}

Try it yourself before checking the explanation above.

If \int_{- 3}^{2} f (x) d x = \frac{7}{3} and \int_{- 3}^{9} f (x) d x = - \frac{5}{6}, then what is the value of \int_{2}^{9} f (x) d x ?

- \frac{19}{6}

\frac{19}{6}

\frac{3}{2}

- \frac{3}{2}

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