Question

Calculate the value of the area between the function f(x)=x^2-4f(x)=x2−4 and the x-axis on the interval from x = 0 to x = 2. round your answer to one decimal place.

Answer 1

When you are asked to find the area under the curve with a given equation, this is an application of integral calculus. The concept is that, any infinitesimal strip under the curve, when added together, equals the area. Thus, integrate the given equation with limits from 0 to 2.

$A = \int\limits^2_0 {(x^{2}-4) } \, dx$

A = [x³/3 - 4x]lim 0->2
A = (2³/3 - 4(2)] - (0³/3 - 4(0)] 
A = 16/3 - 0
A = 16/3 ≈ 5.3 sq. units

Answer 2

To determine the area, calculate first for the differential of the equation given.

          f(x)  = x² - 4

Differentiating,

           f'(x) = 2x

Then, we officially have 2. 
          f'(2) = 2(2) = 4 

          f'(0) = 2(0) = 0

To determine the area, subtract the given answer to get 4 units squared. 

Answer: 4 units/guarrantee