SOLUTION: Hey! :D ive been doing work on areas between curves and axis's but ive stumbled across an area i find difficult! :D i understand how to use integration to find the distan

Question 124501This question is from textbook AS core for edexcel, advanced maths.
: Hey! :D
ive been doing work on areas between curves and axis's
but ive stumbled across an area i find difficult! :D
i understand how to use integration to find the distance under a curve and the x-axis, but the question i have got to, it just isn't working, ive used subtraction but my answers keep logically becoming wrong, and actually becoming wrong. i cant find the correct way :( could any one point me in the correct direction? :D
the quetion is, find these shaded areas using A = (integration sign)) y dx and a method of substituion,
for 10b for example, the curve is, y= root x
it gives a point on the y - axis, (0,4) and this goes across to to meet the curve, and that is the shaded area,
how would i go about finding this out? i filled integration in for 4 and 0, but it isnt workiong :( thanks This question is from textbook AS core for edexcel, advanced maths.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The line y=4 meets the y=sqrt(x) curve at (16,0).
Is the following what you have as the area under
the line,above the curve, and in the 1st Quadrant?
Area = integral from 0 to 16 of 4dx - integral from 0 to 16 of x^(1/2)dx?
= 64 - (2/3)(64)
= (1/3)64
= 21 1/3
=============
Cheers,
Stan H.
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