Since
, we can rewrite the integral as

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:

Both integrals are quite immediate: you only need to use the power rule

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: x = 9
Step-by-Step Solution:
Hypotenuse = 15 units
Base = 12 units
Altitude = x units
Using Pythagoras Theorem,
=> Hypotenuse^2 = Base^2 + Altitude^2
(15)^2 = (12)^2 + x^2
225 = 144 + x^2
225 - 144 = x^2
81 = x^2
x^2 = 81
x = √81
=> x = 9
Therefore, Altitude = 9 units
Their GCF is 6 and the sum is 66
Step-by-step explanation:
Answer:
64%
Step-by-step explanation:
25 - 9 = 16, so 16 of the games were won by Sally's team.
16/25 = 64% of the games were won