Trigonometric Integral Calculator

Work out trigonometric integral instantly with clear inputs, formula shown and shareable results.

About Trigonometric Integral Calculator

Trigonometric integrals use standard antiderivatives: ∫sin kx dx = −cos(kx)/k and ∫cos kx dx = sin(kx)/k. Squared terms need the double-angle identity sin²θ = (1 − cos 2θ)/2 first.

Formulas

Basic forms

∫sin kx dx = −cos(kx)/k, ∫cos kx dx = sin(kx)/k

Squared form

∫sin²kx dx = x/2 − sin(2kx)/(4k)

Worked example

With the default values below, Trigonometric Integral Calculator returns Definite integral of 2.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Integrandone of a·sin(kx), a·cos(kx), a·sin²(kx), a·cos²(kx): a·sin(kx)
Coefficient a: 1
Inner coefficient k: 1
Integrate from 0 to (radians): 3.141593

Results

Definite integral: 2.00000000
Simpson's rule check: 2.00000000
Integrand at the upper limit: 0.00000000
Upper limit in degrees: 180.0000 °

Step by step

1Values used
2Basic forms
3Squared form
4Definite integral= 2.00000000
5Simpson's rule check= 2.00000000
6Integrand at the upper limit= 0.00000000
7Upper limit in degrees= 180.0000 °

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Integrate sin x from 0 to π.

[−cos x] gives −(−1) − (−1) = 2.

Why does sin² need an identity?

There is no elementary antiderivative for the squared form directly; rewriting with cos 2x turns it into two easy terms.