Help with finding areas enclosed by curves

[glad apex]

Kindly help with No.5 part (a)

[verbal pasture]

$$ [ \int_{1}^{4} (y-1)(y-4) ,dy ] $$

[warm jungle]

Tony
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[verbal pasture]

Since x is a function of y now, the ouput form 1 to 4 of (y-1)(y-4) would be negative or equal to zero

Therefore the integral would be negative

[glad apex]

How do you solve it though

[verbal pasture]

Just multiply it out

And then integrate

which will be $$\frac{1}{3}y^3-\frac{5}{2}y^2+5y$$

[warm jungle]

Tony

[verbal pasture]

Plug 4 and 1 in and then subtract them

Result is $$-\frac{3}{2}$$

[warm jungle]

Tony

[glad apex]

This is wrong tho

The answer in the textbook is 9/2

On the negative side

[dreamy finch]

+4y

21 - 37.5+12

[verbal pasture]

Oh ye mb

I was too lazy to write it down haha