Sister Rosetta
Kirk Franklin
Answer: A.) 8
Explanation:
Use u-substitution.
(1) Let u=x^3
By the power rule, du/dx=3x^2
Multiplying by dx and dividing by three, we have du/3=x^2dx
To find the new lower bound of integration, plug the old bound, -3, for x in equation (1). We get u=(-3)^3= -27
Similarly, when the upper bound 3 is plugged in, u=27
Now, replacing f(x^3) with f(u) and x^2dx with du/3:
![\int\limits^{3}_{-3} {x^2f(x^3)} \, dx= \int\limits^{27}_{-27} \frac{f(u)}3 \, du \\=\frac{1}3\left[\int\limits^{0}_{-27} {f(u)} \, du+\int\limits^{27}_{0} {f(u)} \, du \right] (2)\\Observe:\int\limits^{0}_{-27} {f(u)} \, du=\int\limits^{27}_{0} {f(u)} du\; \text{ because f(x) is an even function}\\\text{Substitute the left hand side integral for the RHS in equation (2):}\\=\frac{1}3\left[2\int\limits^{27}_0 {f(u)} du\right]\\=\frac{1}3 (2)(12)=8](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B3%7D_%7B-3%7D%20%7Bx%5E2f%28x%5E3%29%7D%20%5C%2C%20dx%3D%20%5Cint%5Climits%5E%7B27%7D_%7B-27%7D%20%5Cfrac%7Bf%28u%29%7D3%20%5C%2C%20du%20%5C%5C%3D%5Cfrac%7B1%7D3%5Cleft%5B%5Cint%5Climits%5E%7B0%7D_%7B-27%7D%20%7Bf%28u%29%7D%20%5C%2C%20du%2B%5Cint%5Climits%5E%7B27%7D_%7B0%7D%20%7Bf%28u%29%7D%20%5C%2C%20du%20%5Cright%5D%20%282%29%5C%5CObserve%3A%5Cint%5Climits%5E%7B0%7D_%7B-27%7D%20%7Bf%28u%29%7D%20%5C%2C%20du%3D%5Cint%5Climits%5E%7B27%7D_%7B0%7D%20%7Bf%28u%29%7D%20du%5C%3B%20%5Ctext%7B%20because%20f%28x%29%20is%20an%20even%20function%7D%5C%5C%5Ctext%7BSubstitute%20the%20left%20hand%20side%20integral%20for%20the%20RHS%20in%20equation%20%282%29%3A%7D%5C%5C%3D%5Cfrac%7B1%7D3%5Cleft%5B2%5Cint%5Climits%5E%7B27%7D_0%20%7Bf%28u%29%7D%20du%5Cright%5D%5C%5C%3D%5Cfrac%7B1%7D3%20%282%29%2812%29%3D8)
since the value of the first integral of the question = 12, which is given. Although the variable is different than the given (u instead of x), it's still the same integral
Answer:
With regards to coordination, there are problems for many organizations. This could be attributed to the following variables.
Explanation:
- Throughout contact, there seems to be a discrepancy. Language always requires a leader, but it philters down as it came right down. In conversation, there seems to be a shortage of clarification and people like to believe things.
- Under responding to staff has become one of the greatest obstacles. Management teams also prevent listening toward certain staff. People are also hated and certain expectations being denied as well as the same thing is overlooked by individuals.
- The interaction also isn't treated as a managerial position starting from the company strategy to the stage including its team manager as well as superiors. There seems to be a feeling of someone not promoting discussion or sharing of thoughts in society.
- Individuals also presume that everyone else grasps the terminology that they can use. Audiences also lack attention and they almost always avoid concentrating.