Graph the integrand and use areas to evaluate the integral.
-$$\int _ { - 2 } ^ { 7 } 6 d x$$
A) 27
B) 54
C) 9
D) 30

Question

Quizplus · Accepted Answer

The integrand is a constant function $6$, which means the graph is a horizontal line at $y = 6$. The definite integral is equal to the area under this line between $x=-2$ and $x=7$, which is a rectangle with base $b=9$ (distance between $-2$ and $7$) and height $h=6$. Thus, the integral evaluates to $	ext{Area} = bh = 9\cdot 6 = \boxed{54}$.

Graph the Integrand and Use Areas to Evaluate the Integral ∫−276dx\int _ { - 2 } ^ { 7 } 6 d x∫−27​6dx

Graph the Integrand and Use Areas to Evaluate the Integral $\int _ { - 2 } ^ { 7 } 6 d x$