Find the area of the region under the graph of the function
On the interval .

A) sq units
B) sq units
C) sq units
D) sq units

Question

Find the area of the region under the graph of the function ​  ​
On the interval  .
​
A) sq units 
B) sq units 
C) sq units 
D) sq units

Quizplus · Accepted Answer

To find the area under the curve, we need to integrate the function within the limits of integration. Thus, we have to find the definite integral of the given function from -5 to 5.

∫[from -5 to 5] (x^3 - 5x) dx
= [(x^4/4) - (5x^2/2)] [from -5 to 5]
= [(5^4/4) - (5(5^2)/2)] - [(-5^4/4) - (5(-5^2)/2)]
= 625/4

Therefore, the area under the graph of the function on the given interval is 625/4 sq units or approximately 156.25 sq units.

The only choice which matches this value is C.

Find the Area of the Region Under the Graph of the Function