Answer:
(w+4) (w-4)
Step-by-step explanation:
Since
, we can rewrite the integral as
![\displaystyle \int_0^1f(t)\;dt + \int_1^4 f(t)\; dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E1f%28t%29%5C%3Bdt%20%2B%20%5Cint_1%5E4%20f%28t%29%5C%3B%20dt)
Now there is no ambiguity about the definition of f(t), because in each integral we are integrating a single part of its piecewise definition:
![\displaystyle \int_0^1f(t)\;dt = \int_0^11-3t^2\;dt,\quad \int_1^4 f(t)\; dt = \int_1^4 2t\; dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E1f%28t%29%5C%3Bdt%20%3D%20%5Cint_0%5E11-3t%5E2%5C%3Bdt%2C%5Cquad%20%5Cint_1%5E4%20f%28t%29%5C%3B%20dt%20%3D%20%5Cint_1%5E4%202t%5C%3B%20dt)
Both integrals are quite immediate: you only need to use the power rule
![\displaystyle \int x^n\;dx=\dfrac{x^{n+1}}{n+1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20x%5En%5C%3Bdx%3D%5Cdfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D)
to get
![\displaystyle \int_0^11-3t^2\;dt = \left[t-t^3\right]_0^1,\quad \int_1^4 2t\; dt = \left[t^2\right]_1^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E11-3t%5E2%5C%3Bdt%20%3D%20%5Cleft%5Bt-t%5E3%5Cright%5D_0%5E1%2C%5Cquad%20%5Cint_1%5E4%202t%5C%3B%20dt%20%3D%20%5Cleft%5Bt%5E2%5Cright%5D_1%5E4)
Now we only need to evaluate the antiderivatives:
![\left[t-t^3\right]_0^1 = 1-1^3=0,\quad \left[t^2\right]_1^4 = 4^2-1^2=15](https://tex.z-dn.net/?f=%5Cleft%5Bt-t%5E3%5Cright%5D_0%5E1%20%3D%201-1%5E3%3D0%2C%5Cquad%20%5Cleft%5Bt%5E2%5Cright%5D_1%5E4%20%3D%204%5E2-1%5E2%3D15)
So, the final answer is 15.
Answer:
2x10=20 X=2
Step-by-step explanation:
Please mark brainliest
Answer:
if I am right Renee would have 82.00 because Lexi has 13.00 less than Renee and together their money's adds up to 95.00 so if you take 13.00 from 95.00 you will have 82.00 that in my opinion
Answer:
The answer is second one (-2)