NEED HELP PLEASE SOMEONE!!!!

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

Kruka [31]

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

$\frac{\pi}{8}(3+2.77163859753386+2.12132034355964+1.14805029709527+0-1.14805029709527)=3.09955772805315$

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

5 0

2 years ago

Simplify the square root √411

kherson [118]

Answer:

20.27

Step-by-step explanation:

$\sqrt{411} =20.27$

8 0

3 years ago

Read 2 more answers

A researcher is testing a new painkiller that claims to relieve pain in less than 15 minutes, on average.a.State the hypotheses

Ivenika [448]

Answer:

I have a feeling it won't be exactly 15 minutes but it'll be around that time, if it's true.

Step-by-step explanation:

4 0

2 years ago

Wayne has 303 marbles if he gives away 123 of the marbles equally to 3 friends about how many marbles will wayne give each frien

Lera25 [3.4K]

Answer:

Each friend receives 41 marbles, Wayne has 180 marbles left.

Step-by-step explanation:

Wayne starts with 303 marbles total. If he decides to give 123 of his marbles away to his friends, we can subtract this amount from his total to get how many he has left:

303 - 123 = 180 marbles left

We also want to know how many marbles each of his three friends receives. Since he wants to split them equally, we need to divide the number he is giving away by 3:

123 ÷ 3 = 41 marbles a piece to each friend

6 0

3 years ago

Read 2 more answers

5) The graph of the parent linear function f(x) = x is shown in black on the coordinate grid. Write the function that represents

djyliett [7]

Answer:

(m) increased, (b) unchanged. g(x)

(m) decreased, (b) unchanged. m(x)

(m) unchanged, (b) increased. h(x)

(m) unchanged, (b) decreased. n(x)

f(x): m = -1/2 b = 2

g(x): m = 1/3 b = -3

h(x): m = 2 b = 0

8 0

2 years ago