How to solve with integration?
how to do question 10 a) b) and question 3 and 4?
how to do question 10 a) b) and question 3 and 4?
3 Answers
Explanation:
Q is the x-intercept of the line
To find this point, let
So
P is a point of interception between the curve and the line.
Sub
From the graph, the x co-ordinate of P is positive, so we can reject
graph{(2x+y-15)(x^2-y)=0 [-17.06, 18.99, -1.69, 16.33]}
Now for the area
To find the total area of this region, we can find two areas and add them together.
These will be the area under
We can work out the area of the line through integration, but its easier to treat it like a triangle.
For 3 & 4
[Tom's done 10]
Explanation:
3
4
See below:
Warning: Long answer!
Explanation:
For (3):
Using the property:
Hence:
For (4):
(same thing)
However, we must swap the limits on the integral, so:
So:
For 10 (a):
We have two functions intersecting at
(I turned the line function into slope-intercept form)
So
(inputting
So the coordinate of
For
So
For 10 (b).
I will construct two integrals to find the area. I will solve the integrals separately.
The area is:
(Solve first integral)
(substitute the limits into the integrated expression, remember:
Upper-lower limit to find the value of integral)
(solve second integral)
(substitute limits: Upper-lower)