Maths問題請教 , 各位知識朋友 , 入黎幫我手 ar !!!

這是 A Maths 的大題目吧?
有curve sketching 同 Integration...

首先, curve 同 line 的 interception points 係咩意思呢?
即係同時符合兩條式的 (x,y) pair,
可以畫圖睇邊個點同時係兩條線上面，
亦可以 algebraically 運算得出黎。
part (i) 係用格仔紙plot兩條線出黎呢, 即係畫個 table, x 由 -10 到 10, 搵返對應的y, 再mark點點, 再描返條線
part (ii) 係將直線的 y 代落 曲線條式，再 solve 條 x 的二次方程.
你試一試，再對答案.
tips: 做左 (ii) 先做返 (i), 咁樣可以知道幅圖的範圍
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y = 3x^2 + 3x + 10 = 5x + 35
3x^2 -2x -25 =0
determinant = b^2 - 4*a*c = 4 - 300 < 0
都無 solution ge.... =.=" 你睇清楚條題目la...
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iii)Find the volume generated by revolving the area bounded by the curve and the line about the x-axis.
呢題叫我地計 solid of revolution, 即係 int pi*(f(x))^2 dx,
where f(x) = min { 3x^2 + 3x + 10 , 5x + 35 }
boundary 係由 f(x)係 0 到兩條線的交叉點，再到 f(x) 係 0
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part b 又係 solid of revolution, 其實即係 pi*r^2*h
不過個 h 係 dy 或者 dx, 個 r 係 f(y) 或 f(x)
b(i) is straight forward
INT pi*(4x^2 + 3x + 20 )^2 dx
= pi* INT (16*x^4 + 24*x^3 + 169*x^2 + 120*x + 400) dx
= pi* [ 16/5*x^5 + 6*x^4 + 169/3*x^3 + 60*x^2 + 400*x ] from 1 to 5
= a number
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b(ii) is a bit harder,
change x into subject first,
y = 4x^2 + 3x + 20 = 4*x^2 + 2*(2*x)*(3/4) + (3/4)^2 - (3/4)^2 + 20
= ( 2*x + 3/4 )^2 + 20-9/16
x = 1/2* [ +sqrt( y - 20+9/16 ) - 3/4 ]
use this g(y) as r during integration.