1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Harrizon [31]
3 years ago
6

f(x) = 3 cos(x) 0 ≤ x ≤ 3π/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Round your ans

wer to six decimal places.)
Mathematics
1 answer:
Kruka [31]3 years ago
5 0

Answer:

\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558

Step-by-step explanation:

We want to find the Riemann sum for \int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx 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)

where \Delta{x}=\frac{b-a}{n}.

Step 1: Find \Delta{x}

We have that a=0, b=\frac{3\pi }{4}, n=6

Therefore, \Delta{x}=\frac{\frac{3 \pi}{4}-0}{6}=\frac{\pi}{8}

Step 2: Divide the interval \left[0,\frac{3 \pi}{4}\right] into n = 6 sub-intervals of length \Delta{x}=\frac{\pi}{8}

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

Step 3: Evaluate the function at the left endpoints

f\left(x_{0}\right)=f(a)=f\left(0\right)=3=3

f\left(x_{1}\right)=f\left(\frac{\pi}{8}\right)=3 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}=2.77163859753386

f\left(x_{2}\right)=f\left(\frac{\pi}{4}\right)=\frac{3 \sqrt{2}}{2}=2.12132034355964

f\left(x_{3}\right)=f\left(\frac{3 \pi}{8}\right)=3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=1.14805029709527

f\left(x_{4}\right)=f\left(\frac{\pi}{2}\right)=0=0

f\left(x_{5}\right)=f\left(\frac{5 \pi}{8}\right)=- 3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=-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

\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558

You might be interested in
Traveling at an average speed of 50 miles per hour, the trip from point A to point B takes 2 hours. Traveling at an
Anarel [89]

Answer:

option A is the correct answer.

Step-by-step explanation:

4 0
3 years ago
Please help me find surface area for each. Round to the nearest tenth if needed.
Degger [83]

Answer:

168 in², 94.25 yd²

Step-by-step explanation:

I couldn't find a formula for the SA of a triangular prism so I just found the area of each surface.

The formula for SA of a cylinder is 2\pi rh+2\pi r^{2}

All work for triangular prism is in the image

3 0
3 years ago
Help and explain very easy hurry 10 points
stealth61 [152]

Answer:

\$18.97 per hour

Step-by-step explanation:

step 1

Find the total hours

(37 hours/week)*(52 week)=1,924 hours

step 2

Divide the annual salary by the total hours

\frac{36,500}{1,924}= 18.97\frac{\$}{h}

7 0
3 years ago
Factor 60x−8460x−84 using the GCF.
PolarNik [594]
I hope this helps you

6 0
3 years ago
Arrange the following fraction in ascending order 2/3 1/6 3/5<br>​
sladkih [1.3K]
Ascending order just means to be arranged from smallest to largest

Answer: 1/6 2/3 3/5
3 0
3 years ago
Other questions:
  • The histogram below shows the number of hoagie sandwiches students in Carson's class sold for their fundraiser. Use the histogra
    11·1 answer
  • Please answer ASAP!!!! Will give branliest!!!!
    14·2 answers
  • True or False: The Associative Property allows you to change the order of terms in an expression.
    13·2 answers
  • 11 feet 8 inches plus 2 feet 9 inches
    5·2 answers
  • Kia thinks that every number has at least two factors. Which explains whether Kia is correct?
    9·2 answers
  • What are the lengths of the other two sides of the triangle?
    13·2 answers
  • Pls help my cousin I am too lazy to hep her PLSSSSS!!
    11·2 answers
  • PLEASE HELP ME FAST!!! Monica's bicycle wheel has a radius of 16 inches. Kevin's tricycle wheel has a radius of 8 inches. How ma
    7·1 answer
  • 6. Calculate the area of the octagon in the<br> figure below.
    14·1 answer
  • The waiter at El Jarrito brought you the bill. The amount was $53.70. You thought the waiter did the best job you have even seen
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!