Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
secondary 4 | A Maths
2 Answers Below
Anyone can contribute an answer, even non-tutors.
Can anyone solve this question? I only managed to get A (3,0), and B (0, ln2). I’m unsure about my coordinates of C, which I got C (0,-6) and part iv and v.
Date Posted: 3 years ago
Views: 343
C(0,-6) is correct.
okay. I got 3ln2 for (iv), and from there it all went downhill as I can’t prove the area the way it is in the question :(
y = ½ ln(4 - x)
2y = ln (4 - x)
4 - x = e^2y
x = 4 - e^2y
k = 2
2y = ln (4 - x)
4 - x = e^2y
x = 4 - e^2y
k = 2
Hang on. Writing this down.
thanks guys.
The problem is at O level, you're not taught to integrate ln x and its variants yet. So for this question, you have to integrate from the x side.
Notice that the shaded area is made up of a right angled triangle and another part bordered by the axis and the curve.
Notice that the shaded area is made up of a right angled triangle and another part bordered by the axis and the curve.
yeah. I got 9 units^2 for the triangle. trying to solve the curved part
So what we do is to integrate the curve from B to A.
We use the y-coordinate of B as our upper bound , and y-coordinate of A as our lower bound
∫(upper bound ln2, lower bound 0) x dy
= ∫(ln2, 0) (4 - e^2y) dy
= [4y - ½e^2y] (upper bound ln2, lower bound 0)
= (4ln2 - ½e^(2ln2)) - (4(0) - ½e^(2 x 0) )
= 4ln2 - ½e^ln(2²) + ½
= 4ln2 - ½(4) + ½
= 4ln2 - 3/2
We use the y-coordinate of B as our upper bound , and y-coordinate of A as our lower bound
∫(upper bound ln2, lower bound 0) x dy
= ∫(ln2, 0) (4 - e^2y) dy
= [4y - ½e^2y] (upper bound ln2, lower bound 0)
= (4ln2 - ½e^(2ln2)) - (4(0) - ½e^(2 x 0) )
= 4ln2 - ½e^ln(2²) + ½
= 4ln2 - ½(4) + ½
= 4ln2 - 3/2
So add this to 9 units²
9 + 4ln2 - 3/2
= 4ln2 + 7½
= 4ln2 + 7.5
9 + 4ln2 - 3/2
= 4ln2 + 7½
= 4ln2 + 7.5
that’s what I just got! thank you so much for the both of your help :D
See 2 Answers
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
First four parts. Wait for my fifth part which requires some paper spacez
Date Posted:
3 years ago
hey, thank you! for part (v) its fine, haha. I managed to do it with J’s help... thank you though.
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
An idea
Date Posted:
3 years ago
woah. thank you so much for the dedication and for drawing out the diagrams to visualise. I really appreciate your efforts :’). have a good day
360 Tutoring Program