<span>Since it's even, the integral from -7 to -1 is the same as the integral from 1 to 7.
</span><span>think about
x^2
from 0..1,its 1/3
from 0..7 its 7^3/3
from -1..7 its 7^3/3+1/3
</span>
<span>from -7..-1 of x^2 its -1/3+7^3/3 to get this without integrating we just do 7^3/3-1/3 which is the integral from 0..7 minus the integral from 0..1
</span><span>So the integral from 1 to 0 f(x) dx = 5 changes to the integral from 0 to 1 f(x) dx = -5 and you add it to the integral from 0 to 7 which is 1 making -4</span>
Answer:
- (3, 5), (1, 2) and (5, 1)
Step-by-step explanation:
Make three systems with pairs of lines and solve them to work out the vertices.
1) <u>Line 1 and line 2</u>
<u>Double the second equation and subtract equations:</u>
- -3x + 2y - 2(2x + y) = 1 - 2(11)
- -3x - 4x = 1 - 22
- -7x = - 21
- x = 3
<u>Find y:</u>
- 2*3 + y = 11
- 6 + y = 11
- y = 11 - 6
- y = 5
The point is (3, 5)
2) <u>Line 1 and line 3</u>
<u>Triple the second equation and add up equations:</u>
- -3x + 2y + 3(x + 4y) = 1 + 3(9)
- 2y + 12y = 1 + 27
- 14y = 28
- y = 2
<u>Find x:</u>
- x + 4*2 = 9
- x + 8 = 9
- x = 1
The point is (1, 2)
3) <u>Line 2 and line 3</u>
<u>Double the second equation and subtract the equations:</u>
- 2x + y - 2(x + 4y) = 11 - 2(9)
- y - 8y = 11 - 18
- - 7y = - 7
- y = 1
<u>Find x:</u>
- x + 4*1 = 9
- x + 4 = 9
- x = 5
The point is (5, 1)
Answer:
12
Step-by-step explanation:
Hey, do you need to simplify all of them?
