overall accuracy: 85% record: 14 score: 14 if ∫₂⁵ f(x)dx = -5, and ∫₂⁶ f(x)dx = -3, then ∫₅⁶ f(x)dx equals…

overall accuracy: 85% record: 14 score: 14 if ∫₂⁵ f(x)dx = -5, and ∫₂⁶ f(x)dx = -3, then ∫₅⁶ f(x)dx equals -8 2 8 -2 high score board: overall refresh you must have at least 100 to be on the board. # name record

Answer

Explanation:

Step1: Use integral property

We know that $\int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx$. Let $a = 2$, $b = 5$, $c = 6$. So $\int_{2}^{6}f(x)dx=\int_{2}^{5}f(x)dx+\int_{5}^{6}f(x)dx$.

Step2: Rearrange to solve for $\int_{5}^{6}f(x)dx$

We are given $\int_{2}^{5}f(x)dx=- 5$ and $\int_{2}^{6}f(x)dx=-3$. Rearranging the formula from Step 1 gives $\int_{5}^{6}f(x)dx=\int_{2}^{6}f(x)dx-\int_{2}^{5}f(x)dx$.

Step3: Substitute values

Substitute $\int_{2}^{5}f(x)dx=-5$ and $\int_{2}^{6}f(x)dx = - 3$ into the formula: $\int_{5}^{6}f(x)dx=-3-(-5)$.

Step4: Simplify

$-3-(-5)=-3 + 5=2$.