Let's solve the problem step by step: ### Step 1: Understand the Integral as Area \[ \int_{3}^{9} 2 \, dx \] This integral represents the area under the horizontal line \( y = 2 \) from \( x = 3 \) to \( x = 9 \). The area under a constant function over an interval is a rectangle with height 2 and width \( 9 - 3 = 6 \). **Explanation:** The integrand \( 2 \) forms a rectangle above the \( x \)-axis, from \( x = 3 \) to \( x = 9 \). --- ### Step 2: Calculate the Area Area = height × width = \( 2 \times (9 - 3) = 2 \times 6 = 12 \). **Explanation:** The area of the rectangle (which is what the integral represents) is 12. --- ### **Final Answer:** \[ \int_{3}^{9} 2 \, dx = 12 \]