Integration Math Tool

∫ Integration Math Tool definite · indefinite · numerical

📊 symbolic integration · numerical methods · Riemann sums · advanced calculus

∫ Definite Integral

Function f(x) Lower bound (a) Upper bound (b) Method Simpson's Rule Trapezoidal Rule Riemann Sum (Midpoint) Subintervals (n)

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Numerical integration from a to b

∫ Indefinite Integral

Function f(x)

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Symbolic antiderivative + C

📊 Riemann Sum

Function f(x) Lower bound (a) Upper bound (b) Subintervals (n) Point Left Right Midpoint

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Riemann sum approximation

📐 Integration by Parts

u = dv =

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∫ u dv = uv - ∫ v du

∞ Improper Integral

Function f(x) Lower bound (a) Upper bound (b) - use 999 for infinity

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Improper integral with infinite limits

∬ Double Integral

Function f(x,y) x lower x upper y lower y upper Subintervals (n)

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Numerical double integral

📊 Average Value

Function f(x) Lower bound (a) Upper bound (b)

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f_avg = 1/(b-a) ∫ f(x) dx

📏 Arc Length

Function f(x) Lower bound (a) Upper bound (b)

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L = ∫ √(1 + (f'(x))²) dx

🌀 Surface Area

Function f(x) Lower bound (a) Upper bound (b) Axis x-axis y-axis

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S = 2π ∫ f(x) √(1+(f')²) dx

⚖️ Center of Mass

Function f(x) Lower bound (a) Upper bound (b)

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Centroid (x̄, ȳ) of region

∫ Integration Math Tool – 10-in-1
This comprehensive tool provides essential integration functions:

1. Definite Integral – numerical integration using Simpson's, Trapezoidal, or Riemann.
2. Indefinite Integral – symbolic antiderivative of common functions.
3. Riemann Sum – left, right, or midpoint sums.
4. Integration by Parts – ∫ u dv = uv - ∫ v du.
5. Improper Integral – integrals with infinite limits.
6. Double Integral – numerical double integral over a rectangle.
7. Average Value – average of f(x) over [a,b].
8. Arc Length – length of curve y = f(x).
9. Surface Area – area of revolution around x or y axis.
10. Center of Mass – centroid of region under curve.

💡 Tips:
• Use standard math notation: x*x, sin(x), exp(x), log(x), sqrt(x).
• For improper integrals, use a large number (e.g., 999) for infinity.
• All calculations are client-side – no data sent anywhere.
• Perfect for students, engineers, and scientists.

📖 Integration Math Tool – detailed guide

∫ Definite Integral
Numerically approximates ∫ f(x) dx from a to b.
• Simpson's Rule: Most accurate for smooth functions.
• Trapezoidal Rule: Good general-purpose method.
• Riemann Sum: Basic approximation using rectangles.

∫ Indefinite Integral
Finds the antiderivative F(x) + C for common functions including polynomials, sin, cos, exp, log.

📊 Riemann Sum
Approximates the integral using rectangles:
• Left: uses left endpoint of each subinterval.
• Right: uses right endpoint.
• Midpoint: uses the midpoint – most accurate of the three.

📐 Integration by Parts
∫ u dv = uv - ∫ v du. Used for products of functions.

∞ Improper Integral
Integrals with infinite limits or infinite discontinuities. Use a large number (e.g., 999) for infinity.

∬ Double Integral
Numerical double integral over a rectangular region [a,b] × [c,d].

📊 Average Value
f_avg = 1/(b-a) ∫ f(x) dx. The average value of a function over an interval.

📏 Arc Length
L = ∫ √(1 + (f'(x))²) dx. The length of a curve from a to b.

🌀 Surface Area
S = 2π ∫ f(x) √(1+(f')²) dx (x-axis) or S = 2π ∫ x √(1+(f')²) dx (y-axis).

⚖️ Center of Mass
The centroid (x̄, ȳ) of the region under a curve.

⚡ Educational tool · works offline · no server

✅ integration math tool · 10-in-1 · dynamic · no server