f(x)=

Geometrical \;  interpretation \; of  \; Definite \;  integral \; \int_{a}^{b}{ }{f(x)dx

Value of integral

Lower sum

Upper sum

it represents the area bounded by the curve y=f(x), lines x=a, x=b and x-axis

Rohit Singh
KV DRPCAU Pusa
CC by SA

line 1

line2

f(x) = (0.3 * x^(2)) + 3
a = -5 (slider from -5 to 5, step 1)
b = 5 (slider from -5 to 5, step 1)
eq1: x = a
eq2: x = b
A_{1} = Intersect(f, eq1)
A = Intersect(eq1, xAxis)
B = Intersect(eq2, xAxis)
D = Intersect(f, eq2)
g = Segment(A_{1}, A)
h = Segment(D, B)
Number = 100 (slider from 1 to 100, step 1)
c = LowerSum(f(x), a, b, Number)
d = UpperSum(f(x), a, b, Number)
e: d - c
i = Integral(f(x), a, b)
InputBox1 = Textfield(f)
p = Integral(f(x), x)
n: p(a)
o: p(b)
m = false
text3: "Lower sum=" + c + ""
k = false
text4: "Upper sum=" + d + ""
l = false
text5: "Upper sum−Lower sum=" + e + ""
q = Segment(A, B)
text7: "lines \;  x=" + (LaTeX[a]) + " , "
text9: "line  \; x=" + (LaTeX[b]) + ""
j = false
r = false
text1: "\int_{" + (LaTeX[a]) + "}^{" + (LaTeX[b]) + "}{ }(" + (LaTeX[f]) + ")dx=[" + (LaTeX[p]) + "]^{" + (LaTeX[b]) + "}_{" + (LaTeX[a]) + "}\\ =(" + (LaTeX[o]) + ")-(" + (LaTeX[n]) + ")=" + (LaTeX[i]) + ""