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
tino4ka555 [31]
3 years ago
7

How to evaluate definite integral without the fundamental theorem of calculus?

Mathematics
1 answer:
AURORKA [14]3 years ago
7 0
If we can find the antiderivative function
F
(
x
)
of the integrand
f
(
x
)
, then the definite integral
∫
b
a
f
(
x
)
d
x
can be determined by
F
(
b
)
−
F
(
a
)
provided that
f
(
x
)
is continuous.
We are usually given continuous functions, but if you want to be rigorous in your solutions, you should state that
f
(
x
)
is continuous and why.
FTC part 2 is a very powerful statement. Recall in the previous chapters, the definite integral was calculated from areas under the curve using Riemann sums. FTC part 2 just throws that all away. We just have to find the antiderivative and evaluate at the bounds! This is a lot less work.
For most students, the proof does give any intuition of why this works or is true. But let's look at
s
(
t
)
=
∫
b
a
v
(
t
)
d
t
. We know that integrating the velocity function gives us a position function. So taking
s
(
b
)
−
s
(
a
)
results in a displacement.
You might be interested in
En un trabajo manual de una escuela secundaria se necesitan pedazos alambron de 10,12,16,20 cm de largo, sin que sobre ni falte
zhenek [66]
Hola! No se si buscaste antes por aquí pero ya hay una respuesta anterior a esta pregunta y es la opción D
7 0
3 years ago
I need help plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Taya2010 [7]

Answer:

16

Step-by-step explanation:

Since 2+2 is in parenthesis you do that first. So now you have 8/2(4). 8/2= 4. 4*4 = 16

4 0
3 years ago
Square root 15*3sqyare root 81y
Deffense [45]
<span>No simplification exists, Root remains :
</span>sqrt(15y) 
7 0
3 years ago
Factories 54m3n + 81m4n2 b) 15x2y3z + 25x3y2z + 35x2y2z​
Oliga [24]

<u>Part a)</u>

Given the expression

54m^3n\:+\:81m^4n^2

Apply exponent rule:    a^{b+c}=a^ba^c

54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn     ∵ m^4n^2=m^3mnn

Rewrite 81 as 3 · 27

Rewrite 54 as 2 · 27

                             =2\cdot \:27m^3n+3\cdot \:27m^3mnn

Factor out the common term:   27m³n

                              =27m^3n\left(2+3mn\right)      

Therefore,

54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn=27m^3n\left(2+3mn\right)

<u>Part B)</u>

Given the expression

15x^2y^3z+25x^3y^2z+35x^2y^2z

Apply exponent rule:    a^{b+c}=a^ba^c

15x^2y^3z+25x^3y^2z+35x^2y^2z=15x^2y^2yz+25x^2xy^2z+35x^2y^2z

Rewrite as

                                               =3\cdot \:5y^2x^2zy+5\cdot \:5y^2x^2zx+7\cdot \:5y^2x^2z

Factor out common term 5y²x²z

                                                =5y^2x^2z\left(3y+5x+7\right)

Therefore,

15x^2y^3z+25x^3y^2z+35x^2y^2z=5y^2x^2z\left(3y+5x+7\right)

8 0
3 years ago
One kilogram is 2.2 pounds. Complete the tables. What is the interpretation
valentinak56 [21]
You would multiply each kilogram amount by 2.2 to get the point equivalent.
3 0
3 years ago
Other questions:
  • Anita is making Fruit Baskets to sell in her store. She wants each basket to contain the same number of each type of fruit. What
    13·1 answer
  • 4x+13x=119 what does x=?<br> x=7
    9·2 answers
  • At midnight , the temperature in buffalo is 38.3 degrees Fahrenheit. Each hour the temperature decreases by 3.28. What is the te
    12·1 answer
  • Which of these is NOT equivalent to 2^-3
    11·1 answer
  • If angle GEF is thirteen less than five times angle DEG and angle DEF=149⁰, find angle GEF​
    6·1 answer
  • Complete the table of values for y =6-2x
    10·1 answer
  • A recipe requires 3 cups of flour to make 27 dinner rolls. How much flour is needed to make 9 rolls?Mandy runs 4 km in 18 min. S
    8·1 answer
  • Please help me!!<br> I need to get this question
    13·1 answer
  • Ashley earns $5.50 per hour babysitting. She wants to buy a CD
    11·1 answer
  • The perimeter p of the rectangle equals 30. Find the value of X?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!