Atps Calculo

ETAPA - 1

Desafio - A

∫▒(a^3/3+3/a^3 +3/a)da

(1) (2) (3)

∫▒a³/3 da+∫▒3/a³ da+ ∫▒3/a da

(1)

a^4/12+c

(2) -

∫▒3/a³ da = ∫▒〖3.a^(-3) da = 3 a^(-3+1)/(-3+1) = 3 a^(-2)/(-2) 〗 = - 3/(2a^2 )+c

(3)

∫▒3/a da = 3ln|a|+c

a^4/12- 3/〖2a〗^2 +3ln|a|+c

Desafio – B

∫▒〖100+50q〗

1000q+〖50q〗^2/2

1000q+25q^2

10000+1000q+25q^2

C(0) = 10000 + 50q + 25q²

C(0) = 10000 + 50.0 + 25.0²

C(0) = 10.000

Desafio – C

∫_2^4▒〖16,1.e^(0,07.t) 〗.dt

16,1∫_2^4▒e^(0,07.t) .dt

1/0,07.16,1∫_2^4▒e^(0,07.t) .dx

[230.e^0,07.4 ]- [230.e^0,07.2 ]

304,32-264,56

39,76

Desafio - D

∫_(-3)^2▒e^(x/2)

2.∫_(-3)^2▒e^u du

[2.e^(2/2) ]-[2.e^((-3)/2) ]

5,44-0,45

4,99

ETAPA - 2

(I)

∫▒〖(3-t).(t^2-6t) dt〗

-1/2 ∫▒u^4 du

-1/2 . u^5/5+c

- (t^2-6t)^5/10 +c

VERDADEIRO

(II)

∫_0^5▒〖t/√(t+4) dt〗

t.2 √(t+4)-2∫_0^5▒〖(t+4)^(1/2) dt〗

2t √(t+4)-2〖 ((t+4))/(3/2)〗^(3/2)+ c

2t √(t+4)-(4 √((t+4)^3 ))/3+ c

[2.(5) √(5+4)- (4 √((5+4)^3 ))/3]- [2.(0) √(0+4)- (4 √((0+4)^3 ))/3]

-6 - (-10,66)

4,66

VERDADEIRO