Find the total area of the region between the curve and the x-axis.
-$$y = ( x + 2 ) ^ { 3 } ; 0 \leq x \leq 4$$
A) 1280
B) 324
C) 320
D) 96

Question

Quizplus · Accepted Answer

To find the area between a curve and the x-axis, we need to integrate the curve with respect to x from the lower limit to the upper limit.

In this case, the curve is y = (x+2)^3 and the limits are 0 and 4.

So, the area A is given by:

$A = \int_{0}^{4} (x+2)^3 dx$

We can use the power rule to integrate this function:

$A = [\frac{(x+2)^4}{4}]_{0}^{4}$

$A = \frac{(4+2)^4 - (0+2)^4}{4}$

$A = \frac{6^4 - 2^4}{4}$

$A = \frac{1296 - 16}{4}$

$A = 320$

Therefore, the answer is C.

Find the Total Area of the Region Between the Curve y=(x+2)3;0≤x≤4y = ( x + 2 ) ^ { 3 } ; 0 \leq x \leq 4y=(x+2)3;0≤x≤4