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2. Line integral - Wikipedia

   en.wikipedia.org/wiki/Line_integral

   In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. [1] The terms path integral , curve integral , and curvilinear integral are also used; contour integral is used as well, although that is typically reserved for line integrals in the complex plane .

3. Lists of integrals - Wikipedia

   en.wikipedia.org/wiki/Lists_of_integrals

   Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.

4. List of definite integrals - Wikipedia

   en.wikipedia.org/wiki/List_of_definite_integrals

   In mathematics, the definite integral ()is the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the lines x = a and x = b, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total.

5. Conservative vector field - Wikipedia

   en.wikipedia.org/wiki/Conservative_vector_field

   In vector calculus, a conservative vector field is a vector field that is the gradient of some function. [1] A conservative vector field has the property that its line integral is path independent; the choice of path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the ...

6. Integration by parts - Wikipedia

   en.wikipedia.org/wiki/Integration_by_parts

   This visualization also explains why integration by parts may help find the integral of an inverse function f −1 (x) when the integral of the function f(x) is known. Indeed, the functions x(y) and y(x) are inverses, and the integral ∫ x dy may be calculated as above from knowing the integral ∫ y dx.

7. Tangent half-angle substitution - Wikipedia

   en.wikipedia.org/wiki/Tangent_half-angle...

   Finally, as t goes from 1 to +∞, the point follows the part of the circle in the second quadrant from (0, 1) to (−1, 0). Here is another geometric point of view. Draw the unit circle, and let P be the point (−1, 0). A line through P (except the vertical line) is determined by its slope.