Ejercicios De Calculo Integral

8) F(x)=3x^2-x+10 b=x=10 a=x=0

dw= ∫_a^b▒F(x)dx

dw= ∫_0^10▒〖(3x^2 〗-x+10) dxp?

dw=3∫_0^10▒〖x^2 dx-∫_0^10▒〖x dx+10∫_0^10▒dx〗〗

w=[(3x^3)/3 - x^2/2+10x] ∫_0^10

w= [x^3-x^2/2+10x] ∫_0^10

w=[〖10〗^3-〖10〗^2/2+10 (10)]-[0^3-0^2/2+10(0)]

w = 1050 unidades de trabajo

9) DCX)= cx+10)^(2 ) p=$10000

p=(x+10)^2

10000=(x+10)^2

x+10=√10000

x+10=100

x=100-10

x=90

EC=∫_0^90▒〖(x+10)^2 〗 dx - 90 (10000)

Ec=∫_0^90▒〖(x+10)^2 dx-900000〗

Ec=∫_0^90▒〖(x^2+20x+100)dx-900000〗

Ec=∫_0^90▒〖x^2 dx+20 ∫_0^90▒〖x dx+100∫_0^90▒〖dx-900000〗〗〗

Ec=[x^3/3+ (20x^2)/2+100x] ∫_0^90▒〖- 900000〗

Ec= ((90)^3)/3+10(90)^2+100(90)-900000

Ec=333000-900000

Ec=$ 576000

10) Dc x)=1000-0,4x^2

Sc x)=42x

Ec=∫_0^x▒〖Dcx) dx -xp〗

Ep=xp-∫_0^x▒s(x)dx

Dcx=0,4x^2

1000-0,4x^2

Scx=42x

0,4x^2+42x-1000=0

(x=105±√((105)^2-4(1)(-2500)))/(2(1))

x=(-105±145)/2

x=40/2

x=20

s(20)=42 (20) D(20)=1000-0,4(20)^2

s (20)=840 D(20)=840

p=S (20)=D(20)

p=$840

EC=∫_0^20▒〖(1000-0,4x^2 ) dx-840 (20) 〗

EC=1000∫_0^20▒〖dx-0,4∫_0^20▒〖x^2 dx -16800 〗〗

EC=[1000x-(0,4x^3)/3] ∫_0^20 16800

EC=[1000(20) (.0,4 (20)^3)/3]-16800

EC=19992-16800

EC=3192

EP=20 (840)-∫_0^20▒〖42 x dx〗

EP=16800-42∫_0^20▒〖x dx〗

EP=16800- [(42x^2)/2] ∫_0^20

EP=16800- [21x^2 ] ∫_0^20

EP=16800-[21(20)^2-21(0)^2 ]

EP=16800-8400

EP=8400

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