Find the definite integral by computing an area.
-$$\int _ { 1 } ^ { 5 } ( 2 x + 7 ) d x$$
A) 18
B) 9
C) 26
D) 52

Name: Find the definite integral by computing an area. -\[\int _ { 1 } ^ { 5 } ( 2 x + 7 ) d x\] A) 18 B) 9 C) 26 D) 52
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Question

Quizplus · Accepted Answer

The integral represents the area under the line $y = 2x + 7$ from $x = 1$ to $x = 5$. This is a trapezoid with bases $2(1) + 7 = 9$ and $2(5) + 7 = 17$, and height $5 - 1 = 4$. The area is $\frac{1}{2} \times (9 + 17) \times 4 = 52$.

Find the Definite Integral by Computing an Area ∫15(2x+7)dx\int _ { 1 } ^ { 5 } ( 2 x + 7 ) d x∫15​(2x+7)dx

Find the Definite Integral by Computing an Area $\int _ { 1 } ^ { 5 } ( 2 x + 7 ) d x$