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
HELP ME NOW PLEASE................
Akimi4 [234]
The amount of income tax in dollars and cents is $3,895.38
6 0
3 years ago
Error Analysis: Describe the error in the way the difference of the two polynomials is set up and/or
maria [59]

Answer:

  The distributive property is not properly applied to the second polynomial.

Step-by-step explanation:

For whatever reason, it is a common mistake to say that ...

  -(a +b +c) = -a +b +c . . . . WRONG!

Rather, it should be ...

  -(a +b +c) = -a -b -c . . . . CORRECT

6 0
3 years ago
What is 24% as a growth and decay factor
Lisa [10]

Answer:

When given a percentage of growth or decay, determined the growth/decay factor by adding or subtracting the percent, as a decimal, from 1. In general if r represents the growth or decay factor as a decimal then: b = 1 - r Decay Factor. b = 1 + r Growth Factor. A decay of 20% is a decay factor of 1 - 0.20 = 0.

Step-by-step explanation:

5 0
3 years ago
Determine which equations below, when combined with the equation 3x minus 4y equals 2, will form a system with no solutions. cho
kirill115 [55]
The two equations would yield no solution if they are dependent. That means that both equations are equivalent. You can determine this by manipulating the equations through simplification. For example, a dependent equation would be:

3x - 4y = 2
3x/2 - 2y = 1

Another dependent equation is when you multiply the whole equation with a number, say 3.
(3x - 4y = 2)3
9x - 12y = 6
8 0
3 years ago
Step by step 37 ÷ 6951
Helen [10]

Answer:

0.005323

Step-by-step explanation:

Use the algorithm method

7 0
3 years ago
Other questions:
  • Simplify.
    8·1 answer
  • Need help please and thank you
    12·1 answer
  • Liam is riding his bike at a rate of 7 miles per hour he wants to beat his own one day riding record to do so he has to run more
    7·2 answers
  • Evaluate. Write your answer as a fraction in simplest form.<br><br> (1/2) 4
    10·1 answer
  • Which expression is equivalent to t2 – 36?
    11·1 answer
  • The admission prices for a small fair are $1.50 for children and $4.00 for adults. In one day there was $5050 collected. If we k
    5·1 answer
  • PLZ HELP I NEED TO TURN THIS IN IN 10 mins
    15·2 answers
  • Prove why 2,5,8,11 and 14 are not perfect squares?​
    8·2 answers
  • The working out aswell please.
    10·1 answer
  • If a bag contains 16 red, 4 yellow, 20 blue, and eight white balloons, what is the part to whole ratio of red balloons to all ba
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!