Question

If ${\int }_{-3}^{2}f\left(x\right)dx=\frac{7}{3}$ and ${\int }_{-3}^{9}f\left(x\right)dx=-\frac{5}{6},$ then what is the value of ${\int }_2^{9}f\left(x\right)dx$ ?

• A. $-\frac{19}{6}$
• B. $\frac{19}{6}$
• C. $\frac{3}{2}$
• D. $-\frac{3}{2}$

Answer 1

Answer: (A)

Value of the integral ${\int }_2^{9}f(x)dx$
$={\int }_{-3}^{9}f\left(x\right)dx-{\int }_{-3}^{2}f\left(x\right)dx$
Given, ${\int }_{-3}^{9}f\left(x\right)dx=\frac{-5}{6}$ and ${\int }_{-3}^{2}f\left(x\right)dx=\frac{7}{3}$
Putting these values in equation (i)
${\int }_2^{9}f\left(x\right)dx=\frac{-5}{6}-\frac{7}{3}=-\frac{19}{6}$