# Category:Integral Calculus

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This category contains results about **Integral Calculus**.

Definitions specific to this category can be found in Definitions/Integral Calculus.

**Integral calculus** is a subfield of calculus which is concerned with the study of the rates at which quantities accumulate.

Equivalently, given the rate of change of a quantity **integral calculus** provides techniques of providing the quantity itself.

The equivalence of the two uses are demonstrated in the Fundamental Theorem of Calculus.

The technique is also frequently used for the purpose of calculating areas and volumes of curved geometric figures.

## Also see

## Subcategories

This category has the following 46 subcategories, out of 46 total.

### A

### C

- Cauchy Integral Test (3 P)
- Complex Integral Calculus (1 P)

### D

- Darboux's Theorem (2 P)
- Derivative of Arc Length (3 P)
- Dirichlet Integral (6 P)
- Double Integrals (empty)

### E

- Euler Substitutions (5 P)
- Euler's Integral Theorem (3 P)
- Eulerian Logarithmic Integral (empty)

### G

- Gaussian Integral (1 P)

### I

### K

- Kelvin-Stokes Theorem (3 P)

### L

- Lebesgue Integrals (empty)
- Lower Darboux Integral (1 P)

### M

- Method of Indivisibles (empty)

### P

### R

- Riemann-Stieltjes Integral (14 P)

### S

### U

- Upper Darboux Integral (1 P)

### W

- Weierstrass Substitutions (5 P)

## Pages in category "Integral Calculus"

The following 67 pages are in this category, out of 67 total.

### B

### C

- Cauchy Integral Test
- Cauchy-Bunyakovsky-Schwarz Inequality
- Change of Limits of Integration
- Change of Variables Theorem (Multivariable Calculus)
- Complex Riemann Integral is Contour Integral
- Condition for Darboux Integrability
- Continuous Real Function is Darboux Integrable
- Continuously Differentiable Curve has Finite Arc Length

### D

- Darboux's Theorem
- Definite Integral of Even Function
- Definite Integral of Even Function/Corollary
- Definite Integral of Function plus Constant
- Definite Integral of Limit of Uniformly Convergent Sequence of Integrable Functions
- Definite Integral of Odd Function
- Definite Integral of Odd Function/Corollary
- Definite Integral of Uniformly Convergent Series of Continuous Functions
- Derivative of Arc Length
- Dirichlet Integral

### E

### I

- Integrability Theorem for Functions Continuous on Open Intervals
- Integral of Arcsine Function
- Integral of Constant
- Integral of Power
- Integral of Power/Conventional Proof
- Integral of Power/Fermat's Proof
- Integral Resulting in Arcsecant
- Integration by Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration on Polynomials is Linear Operator

### L

- Lebesgue Integrable Function is not necessarily Riemann Integrable
- Lebesgue Integral is Extension of Darboux Integral
- Linear Combination of Integrals
- Linear Combination of Integrals/Indefinite
- Linear Combination of Riemann-Stieltjes Integrals/Integrand
- Linear Combination of Riemann-Stieltjes Integrals/Integrator
- Lobachevsky Integral Formula