Answer:
Your answer is absolutely correct
Step-by-step explanation:
The work would be as follows:
![\int _0^{\sqrt{\pi }}4x^3\cos \left(x^2\right)dx,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=> 4\cdot \int _0^{\sqrt{\pi }}x^3\cos \left(x^2\right)dx\\\\\mathrm{Apply\:u-substitution:}\:u=x^2\\=> 4\cdot \int _0^{\pi }\frac{u\cos \left(u\right)}{2}du\\\\\mathrm{Apply\:Integration\:By\:Parts:}\:u=u,\:v'=\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\int \sin \left(u\right)du\right]^{\pi }_0\\\\](https://tex.z-dn.net/?f=%5Cint%20_0%5E%7B%5Csqrt%7B%5Cpi%20%7D%7D4x%5E3%5Ccos%20%5Cleft%28x%5E2%5Cright%29dx%2C%5C%5C%5C%5C%5Cmathrm%7BTake%5C%3Athe%5C%3Aconstant%5C%3Aout%7D%3A%5Cquad%20%5Cint%20a%5Ccdot%20f%5Cleft%28x%5Cright%29dx%3Da%5Ccdot%20%5Cint%20f%5Cleft%28x%5Cright%29dx%5C%5C%3D%3E%204%5Ccdot%20%5Cint%20_0%5E%7B%5Csqrt%7B%5Cpi%20%7D%7Dx%5E3%5Ccos%20%5Cleft%28x%5E2%5Cright%29dx%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Au-substitution%3A%7D%5C%3Au%3Dx%5E2%5C%5C%3D%3E%204%5Ccdot%20%5Cint%20_0%5E%7B%5Cpi%20%7D%5Cfrac%7Bu%5Ccos%20%5Cleft%28u%5Cright%29%7D%7B2%7Ddu%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3AIntegration%5C%3ABy%5C%3AParts%3A%7D%5C%3Au%3Du%2C%5C%3Av%27%3D%5Ccos%20%5Cleft%28u%5Cright%29%5C%5C%3D%3E%204%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29-%5Cint%20%5Csin%20%5Cleft%28u%5Cright%29du%5Cright%5D%5E%7B%5Cpi%20%7D_0%5C%5C%5C%5C)
![\int \sin \left(u\right)du=-\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0\\\\\mathrm{Simplify\:}4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0:\quad 2\left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0\\\\\mathrm{Compute\:the\:boundaries}:\quad \left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0=-2\\=> 2(-2) = - 4](https://tex.z-dn.net/?f=%5Cint%20%5Csin%20%5Cleft%28u%5Cright%29du%3D-%5Ccos%20%5Cleft%28u%5Cright%29%5C%5C%3D%3E%204%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29-%5Cleft%28-%5Ccos%20%5Cleft%28u%5Cright%29%5Cright%29%5Cright%5D%5E%7B%5Cpi%20%7D_0%5C%5C%5C%5C%5Cmathrm%7BSimplify%5C%3A%7D4%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29-%5Cleft%28-%5Ccos%20%5Cleft%28u%5Cright%29%5Cright%29%5Cright%5D%5E%7B%5Cpi%20%7D_0%3A%5Cquad%202%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29%2B%5Ccos%20%5Cleft%28u%5Cright%29%5Cright%5D%5E%7B%5Cpi%20%7D_0%5C%5C%5C%5C%5Cmathrm%7BCompute%5C%3Athe%5C%3Aboundaries%7D%3A%5Cquad%20%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29%2B%5Ccos%20%5Cleft%28u%5Cright%29%5Cright%5D%5E%7B%5Cpi%20%7D_0%3D-2%5C%5C%3D%3E%202%28-2%29%20%3D%20-%204)
Hence proved that your solution is accurate.

This may look scary, but all you have to do is distribute, first:

Now it's much easier (remember to distribute the negative):

So, the entire thing simplifies to
-2c. NEAT!
To answer this we need to divide 24 by 3/8.
First we need to convert 24 to a fraction.

When dividing fraction, multiply the first fraction by the reciprocal of the second fraction. (A reciprocal is an upside down fraction)

(simplify:) 64
The answer is
64Hopefully this helps! If you have any more questions or don't understand, feel free to DM me, and I'll get back to you ASAP! :)
Lily has saved $ 7
<em><u>Solution:</u></em>
Given that bracelet costs $30
The bracelet Lily would like to buy costs $5 less than 5 times the amount she has saved
Cost of bracelet = $ 30
From given statement,
Cost of bracelet = 5 times the amount she has saved - 5
Let "x" be the amount saved by lily
Cost of bracelet = 5 times x - 5
Here "times" represents multiplication
30 = 5(x) - 5
30 = 5x - 5
30 + 5 = 5x
5x = 35
On dividing 35 by 5 we get 7
x = 7
Thus Lily saved $ 7
To obtain the sample, one can choose the names of 6 students out of a hat from the students in the class using random sampling.
<h3>What is random sampling?</h3>
It should be noted that a simple random sample is a subset of a statistical population where each member of the subset has an equal probability of being chosen.
Systematic sampling is when the sample members from a larger population are selected based on a fixed, periodic interval. If you want to select a random group of 6 students from a population of about 60 using systematic sampling, every 10th person on the list is selected.
Learn more about sampling on:
brainly.com/question/17831271