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Leni [432]
3 years ago
10

prove that if f is integrable on [a,b] and c is an element of [a,b], then changing the value of f at c does not change the fact

that f is integrable or the value of its integral on [a,b]
Mathematics
1 answer:
Neko [114]3 years ago
6 0

Answer with Step-by-step explanation:

We are given that if f is integrable  on [a,b].

c is an element which lie in the interval [a,b]

We have to prove that when we change the value of f at c then the value of f does not change on interval [a,b].

We know that  limit property of an  integral

\int_{a}^{b}f dt=\int_{a}^{c}fdt+\int_{c}^{b} fdt

\int_{a}^{b} fdt=f(b)-f(a)....(Equation I)

Using above property of integral then we get

\int_{a}^{b}fdt=\int_{a}^{c}fdt+\int_{c}^{b} fdt......(Equation II)

Substitute equation I and equation II are equal

Then we get

\int_{a}^{b}fdt= f(c)-f(a)+{f(b)-f(c)}

\int_{a}^{b}fdt=f(c)-f(a)+f(b)-f(c)=f(b)-f(a)

\int_{a}^{c}fdt+\int_{c}^{b}fdt=f(b)-f(a)

Therefore, \int_{a}^{b}fdt=\int_{a}^{c}fdt+\int_{c}^{b}fdt.

Hence, the value of function does not change after changing the value of function at c.

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Answer:

Sonji is 0.5 miles far from the finish line

Step-by-step explanation:

Data provided in the question:

Distance between the Sonji and the finish line = 0.4 miles

Distance run by Sonji back = one tenth of a mile

i.e = \frac{1}{10} miles = 0.1 miles

Hence,

The total distance of Sonji from the finish line will be

= Distance between the Sonji and the finish line + Distance run by Sonji back

= 0.4 miles + 0.1 miles

= 0.5 miles

Hence,

Sonji is 0.5 miles far from the finish line

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3 years ago
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D is the answer 
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What is the slope of the table below?
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3

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Write this ratio As a fraction in lowest terms 30minutes to 50 minutes
omeli [17]

Answer:

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Divide each side by 10 to simplify.

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Solve each system by substitution.
mariarad [96]

Answer:

1) (x, y) = (1, 8)

2) (x, y) =<em>(-2, -4)</em>

3) (x, y) = (3, -1)

Step-by-step explanation:

1) Given the equations;

7x+2y =23  .... 1

6x+y= 14  .... 2

From 2; y = 14-6x

Substitute into 1;

From 1; 7x+2y =23

7x + 2(14-6x) = 23

7x + 28 - 12x = 23

-5x = 23 - 28

-5x = -5

x = 5/5

x = 1

Substitute x = 1 into y = 14-6x

y = 14 - 6 (1)

y - 14 - 6

y = 8

Hence (x, y) = (1, 8)

2) Given

y=-4

y=-3x-10

We will simply equate bith expression and get x;

-3x - 10 = -4

-3x = -4 + 10

-3x = 6

x = 6/-3

x = -2

<em>Hence the solution is (-2, -4)</em>

<em></em>

3) Given the equation

y=-3x+8

y=5x-16

Equate both expressions;

-3x + 8 = 5x - 16

-3x - 5x = -16 - 8

-8x = -24

x = 24/8

x = 3

Substitute x = 3 into y=-3x+8

y = -3(3) + 8

y = -9 + 8

y = -1

Hence the solution (x, y) = (3, -1)

5 0
3 years ago
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