y-stretchfactor

x-intercept

Step

y-stretch factor

(for non-integer value entry)

ystretchfactor: 1
xintercept = 6 (slider from 2 to 6, step 2)
rhs: ((ystretchfactor * 4) * xintercept^(3))
Area = 108 (slider from 1 to 216, step 1)
lhs: (Area * 3)
b = false
a2: (2 * xintercept)
c = false
d = false
text0: "Area = " + (LaTeX[Area]) + " , x-intercept = " + (LaTeX[xintercept]) + " , y-stretch factor = " + (LaTeX[ystretchfactor]) + ""
text2: "" + (LaTeX[Area]) + "  \; = \; " + (LaTeX[ystretchfactor]) + " \int_{0}^{\left( \frac{" + (LaTeX[a2]) + " k}{k+1} \right) }{ \left [ \left( \frac{1}{k^{2}}- 1  \right){x^2}- " + (LaTeX[a2]) + " \left( \frac{1}{k}-1  \right)x \right ] } \; d x"
text3: "  " + (LaTeX[Area]) + " \; = \;" + (LaTeX[ystretchfactor]) + "\;\left(\frac{ 1- k^2}{k^2} \right)   \int_{0}^{\left( \frac{" + (LaTeX[a2]) + "  k}{k+1} \right) }{ {x^2} dx- " + (LaTeX[ystretchfactor]) + "×" + (LaTeX[a2]) + "  \left( \frac{1-k}{k}  \right)\int_{0}^{\left( \frac{ " + (LaTeX[a2]) + "  k}{k+1} \right) }{ {x} dx"
a2_{1}: (2 * xintercept)
text4: "  " + (LaTeX[Area]) + " \; = \;" + (LaTeX[ystretchfactor]) + "\;\left(\frac{ 1- k^2}{k^2} \right)\frac{ 8×" + (LaTeX[xintercept]) + "^3}{3}\left(\frac{  k}{k+1}\right)^3 -  { " + (LaTeX[ystretchfactor]) + "×" + (LaTeX[a2_{1}]) + "  \left( \frac{1-k}{k}  \right) \left( \frac{4×" + (LaTeX[xintercept]) + "^2}{2}  \right)\left( \frac{k}{k+1}  \right)^2"
a2_{3}: (2 * xintercept)
a2_{2}: (2 * xintercept)
text6: "  " + (LaTeX[Area]) + " \; = \;\frac{ " + (LaTeX[ystretchfactor]) + "×\left({1- k}\right)×8×" + (LaTeX[xintercept]) + "^3×k} { 3\left(k+1\right)^2}-\frac{" + (LaTeX[ystretchfactor]) + "×4×" + (LaTeX[xintercept]) + "^3\left(1-k\right)k}{(k+1)^2} "
a2_{4}: (2 * xintercept)
a2_{5}: (2 * xintercept)
a2_{6}: (2 * xintercept)
a2_{7}: (2 * xintercept)
text7: "  " + (LaTeX[Area]) + " \; = \;\frac{ " + (LaTeX[ystretchfactor]) + "×k×\left({1- k}\right)×4×" + (LaTeX[xintercept]) + "^3} { \left(k+1\right)^2}×\left(\frac{2}{3}-1\right) "
a2_{8}: (2 * xintercept)
a2_{9}: (2 * xintercept)
text8: "  " + (LaTeX[Area]) + " \; = \;\frac{ " + (LaTeX[ystretchfactor]) + "×4k\left({k-1}\right)" + (LaTeX[xintercept]) + "^3} {3 \left(k+1\right)^2} "
e = false
a = true
f = false
text1: "" + (LaTeX[Area]) + " \; = \;\int_{0}^{\left( \frac{" + (LaTeX[a2]) + "k}{k+1} \right) }{ \left [" + (LaTeX[ystretchfactor]) + " \left( \frac{x}{k}-" + (LaTeX[xintercept]) + "  \right) ^{2}- " + (LaTeX[ystretchfactor]) + " \left( x-" + (LaTeX[xintercept]) + "  \right) ^{2} \right ] } \; d x"
g = false
h = false
m1 = Factors(324)
m2 = Factors(864)
hcf = GCD(lhs, rhs)
newleft: lhs / hcf
newright: rhs / hcf
coeff1: newright - newleft
coeff2: newright + (newleft * 2)
coeff3: newleft
text5: "" + (LaTeX[newleft]) + "\left({k²+2k+1}\right)=" + (LaTeX[newright]) + "\left({k²-k}\right)\\" + (LaTeX[coeff1]) + "k²-" + (LaTeX[coeff2]) + "k-" + (LaTeX[coeff3]) + "=0"
InputBox1 = Textfield(ystretchfactor)