Find the total area of the region between the curve and the x-axis.
-$$y = 2 x + 7 ; 1 \leq x \leq 5$$
A) 26
B) 18
C) 9
D) 52

Question

Quizplus · Accepted Answer

To find the area between the curve and the x-axis, we need to integrate the equation with respect to x between the limits of x = 1 and x = 5.

The integral of y = 2x + 7 with respect to x is:

∫(2x + 7)dx = x^2 + 7x + C

Using the limits of integration, we plug in 5 for x and then 1, and subtract the results to find the area:

Area = [(5)^2 + 7(5) + C] - [(1)^2 + 7(1) + C]

Simplifying:

Area = (25 + 35 + C) - (1 + 7 + C)

Area = 52

Therefore, the total area between the curve and the x-axis is 52, and the correct answer is D.

Find the Total Area of the Region Between the Curve y=2x+7;1≤x≤5y = 2 x + 7 ; 1 \leq x \leq 5y=2x+7;1≤x≤5