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:
x = 1 , y = 1 and z = 0
Step-by-step explanation:
-2x+2y+3z=0 ------(1)
-2x-y+z=-3 --------(2)
2x+3y+3z=5 ---------(3)
<u>To find the values of x,y and z</u>
(3) - (2)⇒ 2y + 4z = 2
y + 2z = 1 --------(4)
(1) - (2)⇒ 3y +2z =3 ---(5)
(5) - (4)⇒ 2y = 2
y = 1
Substituting the value of y in (4) we get z =0
Substituting the value of y and z in (1) we get x = 1
Therefore x = 1 , y = 1 and z = 0
Answer:
yea i dont know this one bro
Step-by-step explanation:
Answer:
Slope of the line = 2
Step-by-step explanation:
Slope of a line through two points lying on the line 
and 
is given by,
Slope = 
From the figure attached,
Given line is passing through two points (0, 1) and (1, 3).
Therefore, slope of the line will be,
Slope = 
= 2
-20+14m=10m+16
-10m. -10m
-20+4m=16
+20. +20
4m=36
/4. /4
m=9
