Find the definite integral by computing an area.
-$$\int _ { - 3 } ^ { 3 } ( 2 x + 6 ) d x$$
A) 36
B) 18
C) 12
D) 72

Question

Quizplus · Accepted Answer

The integral $\int _ { - 3 } ^ { 3 } ( 2 x + 6 ) d x$ represents the area under the curve of the function $f(x) = 2x + 6$ from $x = -3$ to $x = 3$. To find this area, we can compute the integral directly:$$\begin{align*}\int _ { - 3 } ^ { 3 } ( 2 x + 6 ) d x &= \left[ x^2 + 6x \right] _ { - 3 } ^ { 3 } \&= \left( 3^2 + 6(3) \right) - \left( (-3)^2 + 6(-3) \right) \&= (9 + 18) - (9 - 18) \&= 27 - (-9) \&= 36.\end{align*}$$Therefore, the area under the curve from $x = -3$ to $x = 3$ is 36.

Find the Definite Integral by Computing an Area ∫−33(2x+6)dx\int _ { - 3 } ^ { 3 } ( 2 x + 6 ) d x∫−33​(2x+6)dx

Find the Definite Integral by Computing an Area $\int _ { - 3 } ^ { 3 } ( 2 x + 6 ) d x$