# Maths Question

Watch
Announcements
Thread starter 1 month ago
#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.
0
1 month ago
#2
what have you tried so far, where are you stuck?
0
Thread starter 1 month ago
#3
(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.
0
1 month ago
#4
(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
0
Thread starter 1 month ago
#5
(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
0
1 month ago
#6
(Original post by 121rp)
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
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
0
Thread starter 1 month ago
#7
(Original post by flaurie)

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?
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### How would you describe the quality of the digital skills you're taught at school?

Excellent (32)
9.73%
Okay (97)
29.48%
A bit lacking (119)
36.17%
Not good at all (81)
24.62%