the regions a, b, c, d, and e in the figure below are bounded by the graph of the function f and the x…

the regions a, b, c, d, and e in the figure below are bounded by the graph of the function f and the x - axis. it is given that ∫_{-2}^{2}f(x)dx = 1 and ∫_{0}^{2}f(x)dx = - 6. what is the value of ∫_{-2}^{0}f(x)dx?

the regions a, b, c, d, and e in the figure below are bounded by the graph of the function f and the x - axis. it is given that ∫_{-2}^{2}f(x)dx = 1 and ∫_{0}^{2}f(x)dx = - 6. what is the value of ∫_{-2}^{0}f(x)dx?

Answer

Explanation:

Step1: Use integral property

We know that $\int_{-2}^{2}f(x)dx=\int_{-2}^{0}f(x)dx+\int_{0}^{2}f(x)dx$.

Step2: Rearrange the formula

We can rewrite it as $\int_{-2}^{0}f(x)dx=\int_{-2}^{2}f(x)dx-\int_{0}^{2}f(x)dx$.

Step3: Substitute given values

Given $\int_{-2}^{2}f(x)dx = 1$ and $\int_{0}^{2}f(x)dx=-6$. Then $\int_{-2}^{0}f(x)dx=1-(-6)$.

Step4: Calculate the result

$\int_{-2}^{0}f(x)dx = 7$.

Answer:

$7$