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  2. List of integrals of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see Lists of integrals. For the special antiderivatives involving trigonometric functions, see Trigonometric integral. [1]

  3. Trigonometric integral - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_integral

    Plot of Si(x) for 0x ≤ 8π. Plot of the cosine integral function Ci(z) in the complex plane from −2 − 2i to 2 + 2i. The different sine integral definitions are ⁡ = ⁡ ⁡ = ⁡ .

  4. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    In the integral , we may use = ⁡, = ⁡, = ⁡. Then, = ⁡ ⁡ = ⁡ (⁡) = ⁡ ⁡ = = + = ⁡ +. The above step requires that > and ⁡ > We can choose to be the principal root of , and impose the restriction / < < / by using the inverse sine function.

  5. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    If the function f does not have any continuous antiderivative which takes the value zero at the zeros of f (this is the case for the sine and the cosine functions), then sgn(f(x)) ∫ f(x) dx is an antiderivative of f on every interval on which f is not zero, but may be discontinuous at the points where f(x) = 0.

  6. 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.

  7. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at

  8. Dirichlet integral - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_integral

    [1] [2] This can be seen by using Dirichlet's test for improper integrals. It is a good illustration of special techniques for evaluating definite integrals, particularly when it is not useful to directly apply the fundamental theorem of calculus due to the lack of an elementary antiderivative for the integrand, as the sine integral , an ...

  9. Integral - Wikipedia

    en.wikipedia.org/wiki/Integral

    which means 2/3 is the result of a weighted sum of function values, √ x, multiplied by the infinitesimal step widths, denoted by dx, on the interval [0, 1]. Darboux sums Darboux upper sums of the function y = x 2