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EastWind [94]
3 years ago
9

How do you do this question?

Mathematics
2 answers:
katen-ka-za [31]3 years ago
7 0

Answer:

0

Step-by-step explanation:

∫ sin²(x) cos(x) dx

If u = sin(x), then du = cos(x) dx.

∫ u² du

⅓ u³ + C

⅓ sin³(x) + C

Evaluate between x=0 and x=π.

⅓ sin³(π) − ⅓ sin³(0)

0

Ilya [14]3 years ago
6 0

Answer:

\int\limits^\pi_0 {\sin^2(x)\cos(x)} \, dx=0

Step-by-step explanation:

So we have the integral:

\int\limits^\pi_0 {\sin^2(x)\cos(x)} \, dx

To evaluate this integral, we can use u-substitution. Remember that the derivative of sin(x) is cos(x). So, let u equal sin(x):

u=\sin(x)

Take the derivative of u:

\frac{du}{dx}=\cos(x)

Multiply both sides by dx:

du=\cos(x)dx

So, we can substitute cos(x) x for du.

We can also substitute sin(x) for u. Thus:

So, our integral is now:

\int\limits^\pi_0 {\sin^2(x)(\cos(x)} \, dx)\\

This is equal to:

=\int\limits^\pi_0 {u^2} \, du

However, we also must change our bounds of integration. To do so, substitute in the lower and upper bound into u. So:

u=\sin(x)\\u=\sin(0)=0

And:

u=\sin(x)\\u=\sin(\pi)=0

Therefore, our integral with our new bounds is:

=\int\limits^0_0 {u^2} \, du

Now, note that the integral has the same upper bound and lower bound. Therefore, this means that our integral is going to be 0 since with the same bounds, there will be no area.

Therefore, our answer is 0:

\int\limits^0_0 {u^2} \, du=0

And we're done!

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vitfil [10]
<h2>1)</h2>

(x - 4) {}^{2}  - 28 = 8 \\ (x - 4) {}^{2}  = 8 + 28 \\ (x - 4) {}^{2}  = 36

This must be true for some value of x, since we have a quantity squared yielding a positive number, and since the equation is of second degree,there must exist 2 real roots.

\sqrt{(x - 4) {}^{2} }  =  ± \sqrt{36}  \\x - 4 = ±6 \\ x _{1}- 4 = 6 \:  \:  \:  \:  \:  \:  \: \:  \:  \:  x _{2}- 4 =  - 6 \\ x_{1} = 6 + 4 \:  \:  \:  \:  \:  \:  \:  \:  \:  \: x_{2} =  - 6 + 4 \\ x_{1} = 10 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \: \:  \: x_{2} =  - 2

<h2>2)</h2>

Well he started off correct to the point of completing the square.

(x - 3)  {}^{2}  = 16 \\ x - 3 = ±4 \\  \: x_{1}  - 3 = 4 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: x_{2}  - 3 =  - 4 \\ x_{1}  = 7 \:  \:  \:  \:  \:  \:  \:  \:  \:  \: x_{2}  =  - 1

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10 months ago
Do many fishermen collect worms at night?
stealth61 [152]
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In the first sentence, the direct object is "worms". The correct option among all the options that are given in the question is the third option or option "C".

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natali 33 [55]

Answer:

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Step-by-step explanation:

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Figure AAA is a scale image of figure BBB.
Vadim26 [7]

Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54

<h3>What is a transformation?</h3>

Transformation is the movement of a point from its initial point to a new location. Types of transformation are<em> reflection, rotation, translation and dilation.</em>

Dilation is the increase or decrease in the size of a figure.

Figure A maps to figure B with a scale factor of 4/9, hence:

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Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54

Find out more on transformation at: brainly.com/question/4289712

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