3 integration questions i need help in. (1 Viewer)

[Riot09]

1.find the area bounded by the curve y= square root x+2,the x-axis and the line x=7.

2.find the area enclosed between the cuve y=2 over (x-3)^2,the x-axis and the lines x=0 and x=1.

3.And whats the primitive of 1 over x^2.

the answers are;18units and 1/3units for the 1st two.

thnx,for ur help.

 

[bored of fail 1]

why does your sig say u did your hsc last yr lol

 

[bored of fail 1]

1. think this exact question was asked in the last week.

x intercept of -2

therefore area = integral ( (x+2)^(1/2) ) dx [ from -2..7]

= (2/3) (x+2)^(3/2) [ 7..-2]

= (2/3) [ 9^(3/2) - 0 ]
= (2/3) 9^(3/2)


2. draw the graph, note that y is always positive , as we divide 2 ( positive ) by a square expression ( another positive )

so area = integral 2/ (x-3)^2 dx [ from 1..0]
= integral 2 (x-3)^-2 dx [ 1..0]
= 2 (x-3)^-1 / -1 [ 1..0]
= -2 / (x-3) [ 1..0]
=( -2/ -2 ) - ( -2/-3) = 1 -2/3 = 1/3 unit^2

 

[bored of fail 1]

3 . integral 1/x^2 = integral x^-2 dx =x^-1/ -1 = -1/x +C

 

[ohexploitable]

1. think this exact question was asked in the last week.

Yeah, I remember it too.