Find the definite integral by computing an area.
-$$\int _ { 2 } ^ { 6 } x d x$$
A) 8
B) 16
C) 4
D) 32

Question

Quizplus · Accepted Answer

The definite integral $\int _ { 2 } ^ { 6 } x d x$ represents the area under the curve $y = x$ from $x = 2$ to $x = 6$. This forms a trapezoid with bases of lengths 2 and 6, and height 4. The area of a trapezoid is given by $\frac{1}{2}(b_1 + b_2)h$, so substituting the values gives $\frac{1}{2}(2 + 6) \times 4 = 16$.

Find the Definite Integral by Computing an Area ∫26xdx\int _ { 2 } ^ { 6 } x d x∫26​xdx

Find the Definite Integral by Computing an Area $\int _ { 2 } ^ { 6 } x d x$