Answer:
3.2
Step-by-step explanation:
0.8(4) = 3.2
Answer:
the answer is 40/4
Step-by-step explanation: 7 1/4 3/4 40/4
Answer:
![\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B%5Cfrac%7B3%20%5Cpi%7D%7B4%7D%7D3%20%5Ccos%7B%5Cleft%28x%20%5Cright%29%7D%5C%20dx%5Capprox%203.099558)
Step-by-step explanation:
We want to find the Riemann sum for
with n = 6, using left endpoints.
The Left Riemann Sum uses the left endpoints of a sub-interval:
![\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7Df%28x%29dx%5Capprox%5CDelta%7Bx%7D%5Cleft%28f%28x_0%29%2Bf%28x_1%29%2B2f%28x_2%29%2B...%2Bf%28x_%7Bn-2%7D%29%2Bf%28x_%7Bn-1%7D%29%5Cright%29)
where
.
Step 1: Find ![\Delta{x}](https://tex.z-dn.net/?f=%5CDelta%7Bx%7D)
We have that ![a=0, b=\frac{3\pi }{4}, n=6](https://tex.z-dn.net/?f=a%3D0%2C%20b%3D%5Cfrac%7B3%5Cpi%20%7D%7B4%7D%2C%20n%3D6)
Therefore, ![\Delta{x}=\frac{\frac{3 \pi}{4}-0}{6}=\frac{\pi}{8}](https://tex.z-dn.net/?f=%5CDelta%7Bx%7D%3D%5Cfrac%7B%5Cfrac%7B3%20%5Cpi%7D%7B4%7D-0%7D%7B6%7D%3D%5Cfrac%7B%5Cpi%7D%7B8%7D)
Step 2: Divide the interval
into n = 6 sub-intervals of length ![\Delta{x}=\frac{\pi}{8}](https://tex.z-dn.net/?f=%5CDelta%7Bx%7D%3D%5Cfrac%7B%5Cpi%7D%7B8%7D)
![a=\left[0, \frac{\pi}{8}\right], \left[\frac{\pi}{8}, \frac{\pi}{4}\right], \left[\frac{\pi}{4}, \frac{3 \pi}{8}\right], \left[\frac{3 \pi}{8}, \frac{\pi}{2}\right], \left[\frac{\pi}{2}, \frac{5 \pi}{8}\right], \left[\frac{5 \pi}{8}, \frac{3 \pi}{4}\right]=b](https://tex.z-dn.net/?f=a%3D%5Cleft%5B0%2C%20%5Cfrac%7B%5Cpi%7D%7B8%7D%5Cright%5D%2C%20%5Cleft%5B%5Cfrac%7B%5Cpi%7D%7B8%7D%2C%20%5Cfrac%7B%5Cpi%7D%7B4%7D%5Cright%5D%2C%20%5Cleft%5B%5Cfrac%7B%5Cpi%7D%7B4%7D%2C%20%5Cfrac%7B3%20%5Cpi%7D%7B8%7D%5Cright%5D%2C%20%5Cleft%5B%5Cfrac%7B3%20%5Cpi%7D%7B8%7D%2C%20%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cright%5D%2C%20%5Cleft%5B%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%20%5Cfrac%7B5%20%5Cpi%7D%7B8%7D%5Cright%5D%2C%20%5Cleft%5B%5Cfrac%7B5%20%5Cpi%7D%7B8%7D%2C%20%5Cfrac%7B3%20%5Cpi%7D%7B4%7D%5Cright%5D%3Db)
Step 3: Evaluate the function at the left endpoints
![f\left(x_{0}\right)=f(a)=f\left(0\right)=3=3](https://tex.z-dn.net/?f=f%5Cleft%28x_%7B0%7D%5Cright%29%3Df%28a%29%3Df%5Cleft%280%5Cright%29%3D3%3D3)
![f\left(x_{1}\right)=f\left(\frac{\pi}{8}\right)=3 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}=2.77163859753386](https://tex.z-dn.net/?f=f%5Cleft%28x_%7B1%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%3D3%20%5Csqrt%7B%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B4%7D%20%2B%20%5Cfrac%7B1%7D%7B2%7D%7D%3D2.77163859753386)
![f\left(x_{2}\right)=f\left(\frac{\pi}{4}\right)=\frac{3 \sqrt{2}}{2}=2.12132034355964](https://tex.z-dn.net/?f=f%5Cleft%28x_%7B2%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B4%7D%5Cright%29%3D%5Cfrac%7B3%20%5Csqrt%7B2%7D%7D%7B2%7D%3D2.12132034355964)
![f\left(x_{3}\right)=f\left(\frac{3 \pi}{8}\right)=3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=1.14805029709527](https://tex.z-dn.net/?f=f%5Cleft%28x_%7B3%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B3%20%5Cpi%7D%7B8%7D%5Cright%29%3D3%20%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B4%7D%7D%3D1.14805029709527)
![f\left(x_{4}\right)=f\left(\frac{\pi}{2}\right)=0=0](https://tex.z-dn.net/?f=f%5Cleft%28x_%7B4%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cright%29%3D0%3D0)
![f\left(x_{5}\right)=f\left(\frac{5 \pi}{8}\right)=- 3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=-1.14805029709527](https://tex.z-dn.net/?f=f%5Cleft%28x_%7B5%7D%5Cright%29%3Df%5Cleft%28%5Cfrac%7B5%20%5Cpi%7D%7B8%7D%5Cright%29%3D-%203%20%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B4%7D%7D%3D-1.14805029709527)
Step 4: Apply the Left Riemann Sum formula
![\frac{\pi}{8}(3+2.77163859753386+2.12132034355964+1.14805029709527+0-1.14805029709527)=3.09955772805315](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%7D%7B8%7D%283%2B2.77163859753386%2B2.12132034355964%2B1.14805029709527%2B0-1.14805029709527%29%3D3.09955772805315)
![\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B%5Cfrac%7B3%20%5Cpi%7D%7B4%7D%7D3%20%5Ccos%7B%5Cleft%28x%20%5Cright%29%7D%5C%20dx%5Capprox%203.099558)
Answer:
(-5,9)
Step-by-step explanation:
7 + 2 is 9 so yeah that's it