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[Merged by Bors] - feat(analysis/special_functions/integrals): some simple integration lemmas #6216

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[Merged by Bors] - feat(analysis/special_functions/integrals): some simple integration lemmas #6216

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benjamindavidson
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@benjamindavidson benjamindavidson commented Feb 13, 2021 •
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Integration of some simple functions, including sin, cos, pow, and inv. @ADedecker and I are working on the integrals of some more intricate functions, which we hope to add in a subsequent (series of) PR(s).

With this PR, simple integrals are now computable by norm_num. Here are some examples:

import analysis.special_functions.integrals
open real interval_integral
open_locale real

example : ∫ x in 0..π, sin x = 2 := by norm_num
example : ∫ x in 0..π/4, cos x = sqrt 2 / 2 := by simp
example : ∫ x:ℝ in 2..4, x^(3:ℕ) = 60 := by norm_num
example : ∫ x in 0..2, -exp x = 1 - exp 2 := by simp
example : ∫ x:ℝ in (-1)..4, x = 15/2 := by norm_num
example : ∫ x:ℝ in 8..11, (1:ℝ) = 3 := by norm_num
example : ∫ x:ℝ in 2..3, x⁻¹ = log (3/2) := by norm_num
example : ∫ x:ℝ in 0..1, 1 / (1 + x^2) = π/4 := by simp

integral_deriv_eq_sub' courtesy of @gebner.

@benjamindavidson benjamindavidson added the WIP Work in progress label Feb 13, 2021
@benjamindavidson benjamindavidson changed the title feat(measure_theory/interval_integral): some simple integration lemmas feat(analysis/special_functions/integrals): some simple integration lemmas Feb 18, 2021
@benjamindavidson benjamindavidson added awaiting-review The author would like community review of the PR and removed WIP Work in progress labels Feb 19, 2021
@benjamindavidson benjamindavidson marked this pull request as ready for review February 19, 2021 04:12
@benjamindavidson benjamindavidson mentioned this pull request Feb 22, 2021
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robertylewis
robertylewis reviewed Feb 22, 2021
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This is great!

src/analysis/special_functions/integrals.lean Outdated Show resolved Hide resolved
@sgouezel sgouezel added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Feb 24, 2021
@benjamindavidson benjamindavidson added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Feb 26, 2021
@semorrison
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bors merge

@github-actions github-actions bot added the ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) label Mar 2, 2021
@github-actions github-actions bot removed the awaiting-review The author would like community review of the PR label Mar 2, 2021
bors bot pushed a commit that referenced this pull request Mar 2, 2021
@benjamindavidson
feat(analysis/special_functions/integrals): some simple integration l…
33b6fcb 
…emmas (#6216)

Integration of some simple functions, including `sin`, `cos`, `pow`, and `inv`. @ADedecker and I are working on the integrals of some more intricate functions, which we hope to add in a subsequent (series of) PR(s).

With this PR, simple integrals are now computable by `norm_num`. Here are some examples:
```
import analysis.special_functions.integrals
open real interval_integral
open_locale real

example : ∫ x in 0..π, sin x = 2 := by norm_num
example : ∫ x in 0..π/4, cos x = sqrt 2 / 2 := by simp
example : ∫ x:ℝ in 2..4, x^(3:ℕ) = 60 := by norm_num
example : ∫ x in 0..2, -exp x = 1 - exp 2 := by simp
example : ∫ x:ℝ in (-1)..4, x = 15/2 := by norm_num
example : ∫ x:ℝ in 8..11, (1:ℝ) = 3 := by norm_num
example : ∫ x:ℝ in 2..3, x⁻¹ = log (3/2) := by norm_num
example : ∫ x:ℝ in 0..1, 1 / (1 + x^2) = π/4 := by simp
```
`integral_deriv_eq_sub'` courtesy of @gebner.
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bors bot commented Mar 2, 2021

Build failed (retrying...):

bors bot pushed a commit that referenced this pull request Mar 2, 2021
@benjamindavidson
feat(analysis/special_functions/integrals): some simple integration l…
5c01613 
…emmas (#6216)

Integration of some simple functions, including `sin`, `cos`, `pow`, and `inv`. @ADedecker and I are working on the integrals of some more intricate functions, which we hope to add in a subsequent (series of) PR(s).

With this PR, simple integrals are now computable by `norm_num`. Here are some examples:
```
import analysis.special_functions.integrals
open real interval_integral
open_locale real

example : ∫ x in 0..π, sin x = 2 := by norm_num
example : ∫ x in 0..π/4, cos x = sqrt 2 / 2 := by simp
example : ∫ x:ℝ in 2..4, x^(3:ℕ) = 60 := by norm_num
example : ∫ x in 0..2, -exp x = 1 - exp 2 := by simp
example : ∫ x:ℝ in (-1)..4, x = 15/2 := by norm_num
example : ∫ x:ℝ in 8..11, (1:ℝ) = 3 := by norm_num
example : ∫ x:ℝ in 2..3, x⁻¹ = log (3/2) := by norm_num
example : ∫ x:ℝ in 0..1, 1 / (1 + x^2) = π/4 := by simp
```
`integral_deriv_eq_sub'` courtesy of @gebner.
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bors bot commented Mar 2, 2021

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(analysis/special_functions/integrals): some simple integration lemmas [Merged by Bors] - feat(analysis/special_functions/integrals): some simple integration lemmas Mar 2, 2021
@bors bors bot closed this Mar 2, 2021
@bors bors bot deleted the integration branch March 2, 2021 04:19
bors bot pushed a commit that referenced this pull request Mar 7, 2021
@benjamindavidson
feat(analysis/special_functions/integrals): mul/div by a const (#6357)
9f17db5 
This PR, together with #6216, makes the following possible:
```
import analysis.special_functions.integrals
open real interval_integral
open_locale real

example : ∫ x in 0..π, 2 * sin x = 4 := by norm_num
example : ∫ x:ℝ in 4..5, x * 2 = 9 := by norm_num
example : ∫ x in 0..π/2, cos x / 2 = 1 / 2 := by simp
```
@benjamindavidson benjamindavidson mentioned this pull request Mar 25, 2021
Closed
bors bot pushed a commit that referenced this pull request Mar 27, 2021
@benjamindavidson
feat(test/integration): add examples of computing integrals by simp (#…
879cb47 
…6859)

As suggested in [#6216 (comment)](#6216 (comment)).

The examples added here were made possible by #6216, #6334, #6357, #6597.
b-mehta pushed a commit that referenced this pull request Apr 2, 2021
@benjamindavidson @b-mehta
feat(analysis/special_functions/integrals): some simple integration l…
4256c5b 
…emmas (#6216)

Integration of some simple functions, including `sin`, `cos`, `pow`, and `inv`. @ADedecker and I are working on the integrals of some more intricate functions, which we hope to add in a subsequent (series of) PR(s).

With this PR, simple integrals are now computable by `norm_num`. Here are some examples:
```
import analysis.special_functions.integrals
open real interval_integral
open_locale real

example : ∫ x in 0..π, sin x = 2 := by norm_num
example : ∫ x in 0..π/4, cos x = sqrt 2 / 2 := by simp
example : ∫ x:ℝ in 2..4, x^(3:ℕ) = 60 := by norm_num
example : ∫ x in 0..2, -exp x = 1 - exp 2 := by simp
example : ∫ x:ℝ in (-1)..4, x = 15/2 := by norm_num
example : ∫ x:ℝ in 8..11, (1:ℝ) = 3 := by norm_num
example : ∫ x:ℝ in 2..3, x⁻¹ = log (3/2) := by norm_num
example : ∫ x:ℝ in 0..1, 1 / (1 + x^2) = π/4 := by simp
```
`integral_deriv_eq_sub'` courtesy of @gebner.
b-mehta pushed a commit that referenced this pull request Apr 2, 2021
@benjamindavidson @b-mehta
feat(analysis/special_functions/integrals): mul/div by a const (#6357)
9611486 
This PR, together with #6216, makes the following possible:
```
import analysis.special_functions.integrals
open real interval_integral
open_locale real

example : ∫ x in 0..π, 2 * sin x = 4 := by norm_num
example : ∫ x:ℝ in 4..5, x * 2 = 9 := by norm_num
example : ∫ x in 0..π/2, cos x / 2 = 1 / 2 := by simp
```
b-mehta pushed a commit that referenced this pull request Apr 2, 2021
@benjamindavidson @b-mehta
feat(test/integration): add examples of computing integrals by simp (#…
c0a3fb9 
…6859)

As suggested in [#6216 (comment)](#6216 (comment)).

The examples added here were made possible by #6216, #6334, #6357, #6597.
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