Find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.
\[
y=2 x^{2}-7 x ; y=0 ;-2 \leq x \leq 2
\]
The area, calculated to three decimal places, is $\square$ square units.
Answer
The area, calculated to three decimal places, is \(\boxed{10.667}\) square units.
Step 1 ：The problem is to find the area bounded by the graphs of the equations \(y=2x^2-7x\), \(y=0\) over the interval \(-2 \leq x \leq 2\).
Step 2 ：The area can be found by integrating the function over the given interval. The area is given by the absolute value of the integral, since the area cannot be negative.
Step 3 ：The function to be integrated is \(f = 2x^2 - 7x\).
Step 4 ：The result of the integration is \(32/3\). This is the area bounded by the graphs of the equations over the given interval.
Step 5 ：The area, calculated to three decimal places, is \(\boxed{10.667}\) square units.
