this question is designed to be answered without a calculator. let $int_{-2}^{2}f(x)dx=-6$. if $f(-2)=-2$…

this question is designed to be answered without a calculator. let $int_{-2}^{2}f(x)dx=-6$. if $f(-2)=-2$, then $f(2)=$\n-8.\n-4.\n4.\n12.

this question is designed to be answered without a calculator. let $int_{-2}^{2}f(x)dx=-6$. if $f(-2)=-2$, then $f(2)=$\n-8.\n-4.\n4.\n12.

Answer

Explanation:

Step1: Apply fundamental theorem of calculus

By the fundamental theorem of calculus, $\int_{a}^{b}f'(x)dx=f(b)-f(a)$. Here $a = - 2$, $b = 2$, so $\int_{-2}^{2}f'(x)dx=f(2)-f(-2)$.

Step2: Substitute given values

We know that $\int_{-2}^{2}f'(x)dx=-6$ and $f(-2)=-2$. Substituting these values into the equation $f(2)-f(-2)=\int_{-2}^{2}f'(x)dx$, we get $f(2)-(-2)=-6$.

Step3: Solve for $f(2)$

Simplify the equation $f(2)+2=-6$. Subtract 2 from both sides: $f(2)=-6 - 2=-8$.

Answer:

A. -8