How do you find the volume of a solid that is enclosed by #y=secx#, #x=pi/4#, and the axis revolved about the x axis?
graph{secx [14.24, 14.24, 7.12, 7.12]}
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To find the volume of the solid generated by revolving the region enclosed by the curve ( y = \sec(x) ), the line ( x = \frac{\pi}{4} ), and the xaxis about the xaxis, you would use the method of cylindrical shells.

Determine the limits of integration by finding the points of intersection between ( y = \sec(x) ) and ( x = \frac{\pi}{4} ).

Set up the integral for the volume using the formula for cylindrical shells:
[ V = 2\pi \int_{a}^{b} x \cdot f(x) , dx ]
where ( f(x) ) is the function representing the curve, and ( a ) and ( b ) are the limits of integration.

Integrate the expression obtained in step 2 with respect to ( x ) over the interval determined in step 1.

Evaluate the integral to find the volume of the solid.
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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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