Divide the interval [3, 5] into
subintervals of equal length
.
![[3,5] = \left[3+\dfrac0n,3+\dfrac2n\right] \cup \left[3+\dfrac2n,3+\dfrac4n\right]\cup\left[3+\dfrac4n,3+\dfrac6n\right]\cup\cdots\cup\left[3+\dfrac{2(n-1)}n, 3+\dfrac{2n}n\right]](https://tex.z-dn.net/?f=%5B3%2C5%5D%20%3D%20%5Cleft%5B3%2B%5Cdfrac0n%2C3%2B%5Cdfrac2n%5Cright%5D%20%5Ccup%20%5Cleft%5B3%2B%5Cdfrac2n%2C3%2B%5Cdfrac4n%5Cright%5D%5Ccup%5Cleft%5B3%2B%5Cdfrac4n%2C3%2B%5Cdfrac6n%5Cright%5D%5Ccup%5Ccdots%5Ccup%5Cleft%5B3%2B%5Cdfrac%7B2%28n-1%29%7Dn%2C%203%2B%5Cdfrac%7B2n%7Dn%5Cright%5D)
The right endpoint of the
-th subinterval is
![r_i = 3 + \dfrac{2i}n](https://tex.z-dn.net/?f=r_i%20%3D%203%20%2B%20%5Cdfrac%7B2i%7Dn)
where
.
Then the definite integral is given by the Riemann sum
![\displaystyle \int_3^5 \sqrt{8+x^2} \, dx = \lim_{n\to\infty} \sum_{i=1}^n \sqrt{8+{r_i}^2} \Delta x = \boxed{\lim_{n\to\infty} \frac2n \sum_{i=1}^n \sqrt{17 + \frac{12i}n + \frac{4i^2}{n^2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_3%5E5%20%5Csqrt%7B8%2Bx%5E2%7D%20%5C%2C%20dx%20%3D%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Csum_%7Bi%3D1%7D%5En%20%5Csqrt%7B8%2B%7Br_i%7D%5E2%7D%20%5CDelta%20x%20%3D%20%5Cboxed%7B%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Cfrac2n%20%5Csum_%7Bi%3D1%7D%5En%20%5Csqrt%7B17%20%2B%20%5Cfrac%7B12i%7Dn%20%2B%20%5Cfrac%7B4i%5E2%7D%7Bn%5E2%7D%7D%7D)
Answer:
D. Nine months
Step-by-step explanation:
Simple interest=principal×rate×time
Principal=$1800
Rate=4.5%
Time=?
Interest=$60.75
Simple interest=principal×rate×time
60.75=1800×4.5×t/100
60.75=8100t/100
60.75=81t
t=60.75/81
t=0.75 year
0.75 years=9 months
Answer:
The answer is 21
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Because 8x4 is 32 and 32x2 is 64 so it’s 2
Answer:
x = 67/x^4
Step-by-step explanation:
I did step by step on the whiteboard. I hope it helps!