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
xxTIMURxx [149]
1 year ago
12

express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]

Mathematics
1 answer:
Lemur [1.5K]1 year ago
8 0

The limit as a definite integral on the interval $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π , 4π] is $\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$.

<h3>What is meant by definite integral?</h3>

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$

substitute the values in the above equation, we get

= $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π, 4π],

simplifying the above equation

$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$

To learn more about definite integral refer to:

brainly.com/question/24353968

#SPJ4

You might be interested in
This data set gives the scores of 41 students on a biology exam: {66, 67, 67, 68, 80, 81, 81, 82, 22, 65, 66, 68, 69, 70, 71, 71
bazaltina [42]
C . median
:-D
#2016 #math
3 0
3 years ago
Read 2 more answers
A construction crew must build 4 miles of road in one week. On Monday, they build 12 mile of road. On Tuesday, they build 13 mil
Julli [10]

\frac{19}{6} many more miles of road are left to build .

<u>Step-by-step explanation:</u>

Here we have , A construction crew must build 4 miles of road in one week. On Monday, they build 1/2 mile of road. On Tuesday, they build 1/3 mile of road.  We need to find that  How many more miles of road are left to build . Let's find out:

  • On Monday, they build 1/2 mile of road.
  • On Tuesday, they build 1/3 mile of road.  

Let Miles of road left to build is x So,

⇒ \frac{1}{2} +\frac{1}{3} +x = 4

⇒ x = 4 - (\frac{1}{2} +\frac{1}{3})

⇒ x = 4 - (\frac{1(3)+1(2)}{6} )

⇒ x = 4 - (\frac{5}{6} )

⇒ x =  (\frac{4(6)-5}{6} )

⇒ x =  \frac{24-5}{6}

⇒ x =  \frac{19}{6}

Therefore, \frac{19}{6} many more miles of road are left to build .

5 0
3 years ago
Read 2 more answers
How to simplify an improper and proper fraction((​
Natali5045456 [20]

Answer:

In order to simplify improper fractions

1. Multiply the denominator and the whole number.

2. Add the numerator to the product.

3. Keep the denominator the same.

4. Easily simplify your solution

Step-by-step explanation:

And for proper fractions, just simplify by finding the GCF and divide Numerator by denominator.

Mark me as brainliest!!

Have a nice day!

6 0
3 years ago
What is 30% of 70? Please help.
garik1379 [7]
Hi lovely,

The answer you're looking for is 21.
3 0
3 years ago
Read 2 more answers
Find the GCF of 14a and 28ab
raketka [301]
The GCF would be 14a, because 14a x 1 = 14a, and 14a x 2b = 28ab.
8 0
3 years ago
Other questions:
  • What is the value of x in the equation 2(x-3)+9=3(x+1)+x?<br> x = -3<br> х=-1<br> x = 0<br> х= 3
    11·2 answers
  • What is the answer to y=4x+3 for x= 1,0,1
    8·1 answer
  • Bryan says that only even numbers are composite
    5·2 answers
  • Consider an employee's whose earnings, in dollars, are according to the continuous stream f(t)=5,000e0.1t for t&gt;0, where t is
    14·1 answer
  • Is 2/3(x-4)=1/3(2x-6) a identity
    8·1 answer
  • IS IT 4.5?
    13·1 answer
  • Will give brainliest to whoever answers correctly.
    11·2 answers
  • Which of the following describes how to translate the graph y = lxl to obtain the graph of y = lx + 1l + 1?
    9·1 answer
  • PLEASE HELP !! ILL GIVE 40 POINTS PLUS BRAINLIEST !!
    12·1 answer
  • -1 1/2 *5/6 + 3/14 / 3/7 + 3/2 * 1/2
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!