Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 15 and the x-axis on the interval [–6, 6]. Round off your answer to the nearest integer. Question 15 options:

25,351 units2

149,473 units2

3,758 units2

2,362 units2

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

By using integration formula

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

On integration , we get

=  

=

After simplification and cancellation we get

 =  

on calculation , we get

=

On L.C.M  15

=

= 25 351.2 units²

Conclusion:-

The area of the region between the graph of the given function and the x-axis = 25,351 units²

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step-by-step explanation: