question given ∫₂⁷ f(x) dx = -9 and ∫₇⁹ f(x) ...
question given ∫₂⁷ f(x) dx = -9 and ∫₇⁹ f(x) dx = -11, compute the following integral. ∫₂⁹ f(x) dx
Answer
# Explanation:
## Step1: Use integral property
By the property of definite - integrals $\int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx$ for $a < b < c$. Here, $a = 2$, $b = 7$, $c = 9$, so $\int_{2}^{9}f(x)dx=\int_{2}^{7}f(x)dx+\int_{7}^{9}f(x)dx$.
## Step2: Substitute given values
We know that $\int_{2}^{7}f(x)dx=-9$ and $\int_{7}^{9}f(x)dx=-11$. Substituting these values into the above formula, we get $\int_{2}^{9}f(x)dx=-9+( - 11)$.
## Step3: Calculate the result
$-9+( - 11)=-9 - 11=-20$.
# Answer:
$-20$