Since ![[0,4]=[0,1]\cup(1,4]](https://tex.z-dn.net/?f=%5B0%2C4%5D%3D%5B0%2C1%5D%5Ccup%281%2C4%5D)
, 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:
D. ASA
Step-by-step explanation:
ASA (Angle-Side-Angle) is a proof of congruence when two triangles share two angles and the side between them.
Answer:
h(x)
Step-by-step explanation:
to solve for an inverse, you swap the x and the y and then solve for y
f(x) = 4x^3-8
y = 4x^3 - 8
x = 4y^3 - 8 swap the x and y
now solve for y:
x + 8 = 4y^3
(x + 8)/4 = y^3
1/4x + 8/4 = y^3
1/4x + 2 = y^3
y = ![\sqrt[3]{1/4x + 2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1%2F4x%20%2B%202%7D)
B. V = (26.6)(4.6)
26.6 = l * w
