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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.
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Cual es la de Raiz de 2000
serg [7]

2000 | 2

1000 | 2

500 | 2

250 | 2

125 | 5

25 | 5

5 | 5

1

√2000 = √2².√2².√5².√5

√2000 = 2.2.5√5

√2000 = 20√5

(aproximadamente 44.72135955)

4 0
4 years ago
The radius of the base of a sugar cone is 1.5 inches and the cone is 8 inches tall.
g100num [7]

Answer:

about 18.85 cubic inches of ice cream can fit inside the cone

Step-by-step explanation:

To understand this, you will need to know the formula for a cone's volume which is

πr^2 times h/3

h being the height of the cone

to clarify the equation is pi (3.14) times the radius squared (which means you put it to the power of 2) and you multiply it by the height divided by 3.

Step by step:

π(1.5)^2 times 8/3

put it in a calculator and solve

round according to the problem

hope it helps

3 0
3 years ago
During a period of 80 minutes, a music station played 8 minutes of commercials. What is the ratio of music they played to commer
igomit [66]

Answer:

Step-by-step explanation:

80 minutes.......8 minutes played commercials....that means (80 - 8) = 72 minutes played music

so the ratio of music to commercials is : 72/8 which reduces to 9/1...so the ratio is 9:1 <=== ur answer

** pay attention to the wording, because if it would have asked for the ratio of commercials to music, it would have been 8/72....ratio would be 1:9

8 0
4 years ago
Can anybody help me?
lakkis [162]

You know that 6x+3 equals 45 because the two sides are equal. So you first put the equation 6x+3=45. Then you use the subtraction property of equality and subtract 3 from both sides. This gives you 6x=42. Then you divide 6 from both sides to get you final answer, x=7

8 0
3 years ago
What is the sum of the first 47 terms of the sequence? -215, -201, -187, -173, ...​
Andru [333]

Answer:

5029

Step-by-step explanation:

There is a common difference between consecutive terms, that is

d = - 201 - (- 215) = - 187 - (- 201) = - 173 - (- 187) = 14

This indicates the sequence is arithmetic with sum to n term

=  [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = - 215 and d = 14 , then

=  [ (2 × - 215) + (46 × 14) ]

    = 23.5 (- 430 + 644)

   = 23.5 × 214

   = 5029

6 0
3 years ago
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