Question 64456: Evaluate:
8
(4x2 + 9x - 11) dx
3
(2 decimal places)
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Find the specific antiderivative, f(x), of the function below with the given initial condition. f'(x) = 3x2 - 6x + 5, f(0) = 3.
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Evaluate:
8
(5x2 - 14x - 4) dx
3
(2 decimal places)
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The marginal cost function for producing x units of a certain product is given by:
C'(x) = 8 + 0.05x
Find the total cost incurred by increasing the production level from 100 to 700 units. (2 decimal places)
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Evaluate:
8
(4x2 - 10x + 43) dx
-4
(2 decimal places)
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Find the average value of the function
f(x) = 4x3 - 6x over the interval [0,9].
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Evaluate:
8
(4x^2 + 9x - 11) dx
3
(2 decimal places)
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Integrating get F(x)=(4/3)x^3+(9/2)x^2-11x
Evaluating: F(8)-F(3)= 882.67-43.5=839.17
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Find the specific antiderivative, f(x), of the function below with the given initial condition. f'(x) = 3x2 - 6x + 5, f(0) = 3.
f(x)=x^3-3x^2+5x+C
f(0)=C=3
Therefore: f(x)=x^3-3x^2+5x+3
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Evaluate:
8
(5x2 - 14x - 4) dx
3
(2 decimal places)
Integrate to get:
F(x)=(5/3)x^3-7x^2-4x
f(x)has a zero at 3.06
Evaluate F(8)-F(3.06)=373.33-(-30)=403.33
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The marginal cost function for producing x units of a certain product is given by:
C'(x) = 8 + 0.05x
Find the total cost incurred by increasing the production level from 100 to 700 units. (2 decimal places)
Integrate to get C(x)=8x+0.025x^2
Evaluate:
C(700)-C(100)=17850-1050=16800
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Evaluate:
8
(4x^2 - 10x + 43) dx
-4
(2 decimal places)
Integrate f(x)
F(x)=(4/3)x^3-5x^2+43x
f(x) has a zero at x=0
Integrate from x=-4 to x=0 and from x=0 to x=8
Evaluate:
F(8)-F(0)=706.67
F(0)-F(-4)=337.3
Total definite integral = 1043.9
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Find the average value of the function
f(x) = 4x^3 - 6x over the interval [0,9].
ave=[f(9)-f(0)]/[9-0]
ave=2862/9=318
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Cheers,
Stan H.
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