Lista de integrais

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Calcule as integrais, respostas abaixo
I) Calcule as seguintes integrais.
1.[pic]= [pic]
2.[pic]= [pic]=2x²+2x³+c
3. [pic]=[pic]=[pic]=[pic]
4.[pic]= [pic]=[pic]
5.[pic]=4t-t²/2+c
6.[pic]= [pic]=[pic]=[pic]
7.[pic]
8.[pic]=[pic]
9.[pic]= [pic]=[pic]=[pic]
10.[pic] =[pic]=[pic]
11) [pic]
12) [pic]
13) [pic]
14) [pic]
15) [pic]
16) [pic]
17) [pic]
18) [pic]
19) [pic]
20) [pic]21) [pic]
[pic]
[pic]
3.[pic]
[pic]
5.[pic]
[pic]
[pic]
8)[pic]
[pic]
[pic]

11.[pic]
12. [pic]
13. [pic]
14. [pic]
15. [pic]
16. [pic]
17. [pic]
18. [pic]
19 [pic]
20. [pic]
21. [pic]


II) Encontre as primitivas das seguintes funções compostas:




1) [pic]
[pic]

2) [pic]=
[pic]

3)[pic]
[pic]

4) [pic]

[pic]

5) [pic]
[pic]
6) [pic]
[pic]

7)[pic]
[pic]
8) [pic]
[pic]
9) [pic][pic]
10) [pic]
[pic]
11) [pic]
[pic]
12) [pic]
[pic]
13) [pic]
14) [pic]
[pic]
15)[pic]
[pic]

16)[pic]
[pic]


17) [pic]
[pic]

18)[pic]
[pic]

19) [pic]
[pic]

20)[pic]
[pic]




III) Calcule por frações parciais (A e B):
1)[pic]
=[pic]
A(x+8) + B(x-3) = x
x =3 (A(3+8) + B(3-3) = 3( 11A = 3( A= 3/11
x=-8( A(-8+8) + B(-8-3)=-8 ( -11B= -8(B = 8/11


(=[pic]
2)[pic]
3x2 + 0x +1 |x2-9x +20
-3x2 +27x -60 3
27x-59
x2-9x+20 =0( ( = b2-4.a.c = (-9)2-4.1.20= 81-80=1
x = [pic]=[pic]( x1 = 10/2 =5 e x2 = 8/2 = 4
x2 – 9x+20 = a (x-x1)(x-x2)=1.(x-5).(x-4) = (x-5).(x-4)
[pic]=[pic]
[pic]
A(x-4)+B(x-5) = 27x-59
x = 5 ( A(5-4) + B(5-5) = 27.5 - 59 ( A=76
x = 4 ( A(4-4) +B(4-5) = 27.4 – 59 ( -B = 49( B = -49
(3x+76.ln|x-5|-49.ln|x-4|+k
3.[pic]
=[pic]
A(x-1) + B(x-3) = 5x-2
x =3 (A(3-1) + B(3-3) = 5.3 -2 ( 2A =13( A= 13/2
x=1( A(1-1) + B(1-3)=5.1-2 ( -2B= 3(B = -3/2


(=[pic]
4.[pic]


x2 -7x +12 |x2-7x +6
-x²+7x-6 1
6
x2-7x+6 =(x-6).(x-1)


[pic]=[pic]
[pic]
A(x-1)+B(x-6) = 6
x = 6 ( A(6-1) + B(6-6) = 6 ( A=6/5
x = 1 ( A(1-1) +B(1-6) = 6( B = -6/5
([pic]

5.
[pic]

6.
[pic]

7. [pic]

A(x-2)+Bx = x-1
A(0-2)+B.0=0-1(-2A=-1(A = ½
A(2-2)+B.2 = 2-1( 2B = 1( B=1/2

[pic]=[pic]

8.[pic]
A(2x-3)+B(x+3) = 5x-2
A(2.(-3)-3)+B(-3+3)=5.(-3)-2( -9A = -17( A = 17/9
A(2.(3/2)-3)+B(3/2+3)=5.3/2-2( 9/2B = 11/2( A = 11/9

[pic]

9.[pic]
A(7x+2)+B(3x-1)=4x+5
A(7(-2/7)+2)+B(3(-2/7)-1)= 4(-2/7)+5( B.(-13/7) =27/7( B = -27/13
A(7.(1/3)+2)+B(3(1/3)-1)= 4(1/3)+5( A.(13/3) = 19/3(A =19/13

[pic]

10) [pic]=[pic]= [pic]

A(5x-4)+B(2x+1)=1
A(5.(-1/2)-4) +B (2.(-1/2)+1) = 1( A(-13/2)=1( A = -2/13
A(5.(4/5)-4) +B (2.(4/5)+1) = 1( B(13/5)=1( A = 5/13


[pic][pic]

11) [pic]=[pic]= A . ln|x-1|+B. ln|x-3| +k

5 = A(x-3)+B(x-1)
x = 1( 5 = A(1-3)+B(1-1)( 5= A .(-2) +B.0 ( 5 = -2A (2A =-5( A =-5/2
x = 3( 5 = A(3-3)+B(3-1)( 5= A.0 +B.2( 5= 2B ( 2B =5( B = 5/2
Logo, [pic]= -5/2 ln|x-1| + 5/2.ln|x-3| +k

12)[pic]

1x3 + x2 + 2x + 3 |x2-3x +2
-1x3 + 3x2 -2x x + 4
4x2 + 0x +3
-4x2 +12x -8
12x -5
[pic]=[pic]=[pic]=[pic]= [pic]+[pic]=[pic].
12x-5= A(x-2)+B(x-1)
x = 1( 12.1-5 = A(1-2)+B(1-1)(7 = -A( A = -7
x = 2 ( 12.2-5 =A(2-2)+B(2-1) (19 = B.1(B=19
Logo[pic]= [pic]

13) [pic]
x2-5x+6 =0( ( = b2-4.a.c = (-5)2-4.1.6= 25-24=1
x = [pic]=[pic]( x1 = 6/2 = 3 e x2 = 4/2 = 2
x2 –5x+6 = a (x-x1)(x-x2) =1.(x-3).(x-2) = (x-3).(x-2)
[pic]=[pic]=[pic]=A.ln|x-3| + B.ln|x-2|+k
2x = A(x-2)+B(x-3)
x = 3( 2.3 = A(3-2)+B(3-3)( 6= A.1 +B.0( 6 = A ( A = 6
x = 2( 2.2 = A(2-2)+B(2-3)( 4= A.0+B(-1)( 4 = -B( B = -4...
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