What is the arc length of teh curve given by #f(x)=3x^6 + 4x# in the interval #x in [2,184]#?
To find arc length, we use the equation:
Now plug into the formula with the interval:
Solve inside the parentheses:
Simplify inside the square root:
Solve the integral:
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To find the arc length of the curve given by (f(x) = 3x^6 + 4x) in the interval (x \in [2, 184]), you can use the formula for arc length:
[ L = \int_{a}^{b} \sqrt{1 + (f'(x))^2} , dx ]
where (f'(x)) is the derivative of (f(x)). Calculate the derivative of (f(x)), then substitute it into the formula. Finally, integrate the expression over the given interval ([2, 184]).
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To find the arc length of the curve given by ( f(x) = 3x^6 + 4x ) in the interval ( x ) in ([2, 184]), you use the formula for arc length:
[ L = \int_{a}^{b} \sqrt{1 + (f'(x))^2} , dx ]
Where ( f'(x) ) is the derivative of ( f(x) ).

Find the derivative of ( f(x) ). [ f'(x) = 18x^5 + 4 ]

Compute ( \sqrt{1 + (f'(x))^2} ). [ \sqrt{1 + (f'(x))^2} = \sqrt{1 + (18x^5 + 4)^2} ]

Integrate ( \sqrt{1 + (f'(x))^2} ) from (2) to (184). [ L = \int_{2}^{184} \sqrt{1 + (18x^5 + 4)^2} , dx ]

Calculate the definite integral to find the arc length.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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