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2 years ago

The average value of the function y = x² – 1 on [0, 12] is

Mathematics

1 answer:

shusha [124]2 years ago

3 0

Answer:

47.

Step-by-step explanation:

1) the rule:

$f_{avr}=\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx ,$

where a;b are 0 and 12, f(x)=x²-1.

2) according to the rule above:

$f_{avr}=\frac{1}{12-0} \int\limits^{12}_0 {(x^2-1)} \, dx=\frac{1}{12}(\frac{x^3}{3}-x)|^{12}_0=48-1=47.$

You might be interested in

Question :

Darya [45]

Answer:

1156

Step-by-step explanation:

We know that,

( a + b ) ² = a² + 2ab + b²

We can follow the same method to find the value of this.

12² + 22²

( 12 + 22 ) ²

12² + 2 × 12 × 22 + 22²

144 + 24 × 22 + 484

144 + 528 + 484

672 + 484

Let me know if you have any other questions. :)

6 0

2 years ago

Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

$|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2$

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

3 0

2 years ago

How would you write 0.000345 liter in scientific notation?

Bumek [7]

I think this is right but, 0.000345 = 3.45x10^-4

4 0

2 years ago

Please give me the explanation so I KNOW that it's right? Thanks.

MrMuchimi

Answer:

its A, B, C or D

Step-by-step explanation:

it has to be one of them.

5 0

3 years ago

Class a had a mean score of 7.8 and a standard deviation of 1 class b had a mean score of 8.1 and a standard deviation of 0.2 wh

Karo-lina-s [1.5K]

Class 2 scored better on average

<h3>How to determine which class scored better on average?</h3>

The averages and the standard deviations are given as:

Class 1

Mean score = 7.8

Standard deviation = 1

Class 2

Mean score = 8.1

Standard deviation = 0.2

As a general rule, the smaller the standard deviation; the better the average

Class 2 has a smaller deviation

Hence, class 2 scored better on average

Read more about standard deviation at:

brainly.com/question/28061243

#SPJ1

6 0

1 year ago