Answer:
no i can not
Step-by-step explanation:
Answer:
8.727
Step-by-step explanation:
Since the below edge, d = 15 cm, and the height, h = 12.2 cm, we will use the Pythagorean theorem to find the distance r.
![d^2=r^2+h^2](https://tex.z-dn.net/?f=d%5E2%3Dr%5E2%2Bh%5E2)
![(15)^2 = r^2+(12.2)^2](https://tex.z-dn.net/?f=%2815%29%5E2%20%3D%20r%5E2%2B%2812.2%29%5E2)
![r^2 = (15)^2-(12.2)^2=225-148.84=76.16](https://tex.z-dn.net/?f=r%5E2%20%3D%20%2815%29%5E2-%2812.2%29%5E2%3D225-148.84%3D76.16)
![r=\sqrt{76.16}=8.727](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B76.16%7D%3D8.727)
Answer:
The area of the region is 25,351
.
Step-by-step explanation:
The Fundamental Theorem of Calculus:<em> if </em>
<em> is a continuous function on </em>
<em>, then</em>
![\int_{a}^{b} f(x)dx = F(b) - F(a) = F(x) | {_a^b}](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D%20f%28x%29dx%20%3D%20F%28b%29%20-%20F%28a%29%20%3D%20F%28x%29%20%7C%20%20%7B_a%5Eb%7D)
where
is an antiderivative of
.
A function
is an antiderivative of the function
if
![F^{'}(x)=f(x)](https://tex.z-dn.net/?f=F%5E%7B%27%7D%28x%29%3Df%28x%29)
The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.
To find the area of the region between the graph of the function
and the x-axis on the interval [-6, 6] you must:
Apply the Fundamental Theorem of Calculus
![\int _{-6}^6(x^5+8x^4+2x^2+5x+15)dx](https://tex.z-dn.net/?f=%5Cint%20_%7B-6%7D%5E6%28x%5E5%2B8x%5E4%2B2x%5E2%2B5x%2B15%29dx)
![\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int _{-6}^6x^5dx+\int _{-6}^68x^4dx+\int _{-6}^62x^2dx+\int _{-6}^65xdx+\int _{-6}^615dx](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3ASum%5C%3ARule%7D%3A%5Cquad%20%5Cint%20f%5Cleft%28x%5Cright%29%5Cpm%20g%5Cleft%28x%5Cright%29dx%3D%5Cint%20f%5Cleft%28x%5Cright%29dx%5Cpm%20%5Cint%20g%5Cleft%28x%5Cright%29dx%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E6x%5E5dx%2B%5Cint%20_%7B-6%7D%5E68x%5E4dx%2B%5Cint%20_%7B-6%7D%5E62x%5E2dx%2B%5Cint%20_%7B-6%7D%5E65xdx%2B%5Cint%20_%7B-6%7D%5E615dx)
![\int _{-6}^6x^5dx=0\\\\\int _{-6}^68x^4dx=\frac{124416}{5}\\\\\int _{-6}^62x^2dx=288\\\\\int _{-6}^65xdx=0\\\\\int _{-6}^615dx=180\\\\0+\frac{124416}{5}+288+0+18\\\\\frac{126756}{5}\approx 25351.2](https://tex.z-dn.net/?f=%5Cint%20_%7B-6%7D%5E6x%5E5dx%3D0%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E68x%5E4dx%3D%5Cfrac%7B124416%7D%7B5%7D%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E62x%5E2dx%3D288%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E65xdx%3D0%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E615dx%3D180%5C%5C%5C%5C0%2B%5Cfrac%7B124416%7D%7B5%7D%2B288%2B0%2B18%5C%5C%5C%5C%5Cfrac%7B126756%7D%7B5%7D%5Capprox%2025351.2)
F(x) = ㏑(x² - 4)
Domain: {-2 ≤ x ≤ 2}, or [-2, 2]
Answer:
C
Step-by-step explanation: