Find the area of the shaded region bounded by y=1x2+x , x = 2, x = 4, and the x-axis. (1 point) Responses 254 25 4 298 29 8 212 21 2 434 43 4 1018 101 8
To find the area of the shaded region, we need to find the definite integral of the function y = x^2 + x from x = 2 to x = 4.
First, find the antiderivative of the function:
∫(x^2 + x) dx = 1/3x^3 + 1/2x^2 + C
Next, evaluate the antiderivative from x = 2 to x = 4:
[1/3(4)^3 + 1/2(4)^2] - [1/3(2)^3 + 1/2(2)^2]
= [64/3 + 32] - [8/3 + 4]
= 212/3
Therefore, the area of the shaded region is 212/3 square units.