Pi really goes on for infinity, but here are the first seven numbers:
3.14159
Basically you need to multiply the percent by the number.
Answer:
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
![F(x) = \int\limits^a_b {f(x)} \, dx](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Cint%5Climits%5Ea_b%20%7Bf%28x%29%7D%20%5C%2C%20dx)
By using integration formula
![\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c](https://tex.z-dn.net/?f=%5Cint%7Bx%5En%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bx%5E%7Bn%2B1%7D%20%7D%7Bn%2B1%7D%20%2Bc)
Given x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]
![\int\limits^6_^-6} (x^{5} + 8 x^{4} + 2 x^{2} + 5 x + 15) )dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E6_%5E-6%7D%20%28x%5E%7B5%7D%20%20%2B%208%20x%5E%7B4%7D%20%20%2B%202%20x%5E%7B2%7D%20%20%2B%205%20x%20%2B%2015%29%20%29dx)
<em>On integration , we get</em>
= ![(\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx%5E%7B6%7D%20%7D%7B6%7D%20%2B%20%5Cfrac%7B8%20x%5E%7B5%7D%20%7D%7B5%7D%20%2B%202%20%5Cfrac%7Bx%5E%7B3%7D%20%7D%7B3%7D%20%2B%5Cfrac%7B5%20x%5E%7B2%7D%20%7D%7B2%7D%20%2B%2015%20x%29%5E%7B6%7D%20_%7B-6%7D)
![F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Cint%5Climits%5Ea_b%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%3D%20F%28b%29%20-F%28a%29)
= ![(\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%5E%7B6%7D%20%7D%7B6%7D%20%2B%20%5Cfrac%7B8%206%5E%7B5%7D%20%7D%7B5%7D%20%2B%202%20%5Cfrac%7B6%5E%7B3%7D%20%7D%7B3%7D%20%2B%5Cfrac%7B5%206%5E%7B2%7D%20%7D%7B2%7D%20%2B%2015X%206%29%20-%20%28%28%5Cfrac%7B%28-6%29%5E%7B6%7D%20%7D%7B6%7D%20%2B%20%5Cfrac%7B8%20%28-6%29%5E%7B5%7D%20%7D%7B5%7D%20%2B%202%20%5Cfrac%7B%28-6%29%5E%7B3%7D%20%7D%7B3%7D%20%2B%5Cfrac%7B5%20%28-6%29%5E%7B2%7D%20%7D%7B2%7D%20%2B%2015%20%28-6%29%29)
After simplification and cancellation we get
= ![\frac{2 X 8 X (6)^{5} }{5} + \frac{2 X 2 X (6)^3}{3} + 2 X 15 X 6](https://tex.z-dn.net/?f=%5Cfrac%7B2%20X%208%20X%20%286%29%5E%7B5%7D%20%7D%7B5%7D%20%2B%20%5Cfrac%7B2%20X%202%20X%20%286%29%5E3%7D%7B3%7D%20%2B%202%20X%2015%20X%206)
on calculation , we get
= ![\frac{124,416}{5} + \frac{864}{3} + 180](https://tex.z-dn.net/?f=%5Cfrac%7B124%2C416%7D%7B5%7D%20%2B%20%5Cfrac%7B864%7D%7B3%7D%20%2B%20180)
On L.C.M 15
= ![\frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B124%2C416%20X%203%20%2B%20864%20X%205%20%2B%20180%20X%2015%7D%7B15%7D)
= 25 351.2 units²
<u><em>Conclusion</em></u>:-
<em>The area of the region between the graph of the given function and the x-axis = 25,351 units²</em>
No you do not. I think I will help.