121rp
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#1
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#1
This question has two parts. Hope someone can help!
Find the equation of the straight line that is normal to the curve y=x^2+x^(4/3) at x=1.
Determine area of region bounded by the curve, normal and the x axis.
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flaurie
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#2
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#2
what have you tried so far, where are you stuck?
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121rp
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#3
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(Original post by flaurie)
what have you tried so far, where are you stuck?
So I took the derivative of the curve. Evaluated at x=1 for the gradient. Got my pt (1,2) and then solved for the equation of line. Although not sure how to get from the tangent to normal.
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flaurie
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(Original post by 121rp)
So I took the derivative of the curve. Evaluated at x=1 for the gradient. Got my pt (1,2) and then solved for the equation of line. Although not sure how to get from the tangent to normal.
gradient of tangent * gradient of normal = -1
(i.e. so if the gradient of the tangent was -7/2 then the gradient of the normal would be 2/7)
then you can sub in the (1,2) for the equation of the line
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121rp
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#5
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(Original post by flaurie)
gradient of tangent * gradient of normal = -1
(i.e. so if the gradient of the tangent was -7/2 then the gradient of the normal would be 2/7)
then you can sub in the (1,2) for the equation of the line
So that'd get me 10y=-3x+23.
For the 2nd part, would I add 2 separate definite integrals together? One for the straight line and another for the curve? Or could I combine them as normal into one integral to solve
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flaurie
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#6
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(Original post by 121rp)
So that'd get me 10y=-3x+23.
:yy:
For the 2nd part, would I add 2 separate definite integrals together? One for the straight line and another for the curve? Or could I combine them as normal into one integral to solve
i find it easiest to split it up into an area under a curve (use integration) and a triangle (1/2*b*h) and add these together
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121rp
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#7
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(Original post by flaurie)
:yy:

i find it easiest to split it up into an area under a curve (use integration) and a triangle (1/2*b*h) and add these together
Right, that makes a lot more sense. I've followed that through and got a value of 52/7 units^2? Would that be right?
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