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
sweet [91]
3 years ago
6

\int\limits^0_∞ cos{x} \, dx

Mathematics
1 answer:
JulijaS [17]3 years ago
7 0

Answer:

\displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty)

General Formulas and Concepts:

<u>Pre-Calculus</u>

  • Unit Circle
  • Trig Graphs

<u>Calculus</u>

  • Limits
  • Limit Rule [Variable Direct Substitution]:                                                     \displaystyle \lim_{x \to c} x = c
  • Integrals
  • Integration Rule [Fundamental Theorem of Calculus 1]:                             \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)
  • Trig Integration
  • Improper Integrals

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \int\limits^0_\infty {cos(x)} \, dx

<u>Step 2: Integrate</u>

  1. [Improper Integral] Rewrite:                                                                         \displaystyle  \lim_{a \to \infty} \int\limits^0_a {cos(x)} \, dx
  2. [Integral] Trig Integration:                                                                             \displaystyle  \lim_{a \to \infty} sin(x) \bigg| \limits^0_a
  3. [Integral] Evaluate [Integration Rule - FTC 1]:                                               \displaystyle  \lim_{a \to \infty} sin(0) - sin(a)
  4. Evaluate trig:                                                                                                 \displaystyle  \lim_{a \to \infty} -sin(a)
  5. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  -sin(\infty)

Since we are dealing with infinity of functions, we can do a numerous amount of things:

  • Since -sin(x) is a shift from the parent graph sin(x), we can say that -sin(∞) = sin(∞) since sin(x) is an oscillating graph. The values of -sin(x) already have values in sin(x).
  • Since sin(x) is an oscillating graph, we can also say that the integral actually equates to undefined, since it will never reach 1 certain value.

∴  \displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty) \ or \ \text{unde}\text{fined}

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Improper Integrals

Book: College Calculus 10e

You might be interested in
HUDSON HAS TO FILL A POT WITH 1 QUART OF WATER. ALL HE HAS IS 1/4 CUP MEASURING CUP. HOW MANY TIMES DOES HE HAVE TO FILL THE 1/4
Marta_Voda [28]
There are 4 cups in a quart.

So if Hudson has only a 1/4 measuring cup, this can be represented by the equation:

4/1/4, solving it we get: 4* 4 (dividing turns a fraction into its reciprocal)

So, 4*4=16

Hudson will have to fill the 1/4 measuring cup 16 times to get a quart.

I hope this helps!
4 0
3 years ago
Read 2 more answers
Please help me find f
vichka [17]
A I think I am not 100% right
6 0
3 years ago
Your favorite video game just went on sale for 33% off.
abruzzese [7]

Answer:

$40.20

Step-by-step explanation:

60 / 100 = 0.6

0.6 x 33 = 29.8

60 - 29.8 = 40.2

Thus he price after the discount would be $40.20

3 0
3 years ago
Select expressions that are equivalent to 5x - 15 - 20x + 10
nordsb [41]

Answer:

-15x - 5

Step-by-step explanation:

5x - 15 - 20x + 10

5x - 20x - 15 + 10

-15x - 5

8 0
3 years ago
Help please. <br><br> Please <br><br> Please
iragen [17]

2x - 6 = 60 - x  \\ add \: x \: to \:both \: sides \\  2x + x - 6 = 60 - x + x \\ 3x - 6 = 60 \\ add \: 6 \: to \: both \: sides \\ 3x - 6 + 6 = 60 + 6 \\ 3x = 66 \\ divide \: both \: sides \: by \: 3 \\  \frac{3x}{3}  =  \frac{66}{3}  \\ x = 22

8 0
3 years ago
Other questions:
  • Jackson says he has an odd number of model cars. He has 6 cars on one shelf and 8 cars on another shelf. Is Jackson correct? Exp
    15·1 answer
  • PLEASE PLEASE HELP ME<br>ASAP!!!!!​
    7·1 answer
  • The circumference of a sphere was measured to be 78 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the ma
    7·1 answer
  • Geometry help!! 10 points!
    6·1 answer
  • A coin and a normal dice is rolled. how many possible outcomes are there
    10·1 answer
  • How to write an equation for functions
    12·2 answers
  • 42,32,30,32,44,36,45,43<br> What is the median
    14·1 answer
  • Please help me I'm stuck on these.. Thanks​
    15·1 answer
  • Find the slope of the line that is ​(a) parallel and ​(b) perpendicular to the line through the pair of points. ​(−5​,−4​) and ​
    5·1 answer
  • write the equation of the line in either form (slope intercept or point slope form) that contains points (4,-5) (8,1)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!