question find ∫₂⁷ (-2x + 7)dx

Explanation:

Step1: Find antiderivative

The antiderivative of $-2x + 7$ is $-x^{2}+7x+C$. Here we can ignore $C$ for definite - integral calculation.

Step2: Apply fundamental theorem of calculus

$\int_{2}^{7}(-2x + 7)dx=\left[-x^{2}+7x\right]_{2}^{7}=(-7^{2}+7\times7)-(-2^{2}+7\times2)$.

Step3: Simplify the expression

$(-49 + 49)-(-4 + 14)=0 - 10=-10$.

Answer:

$-10$