Essays on Integrals

Integration by parts

Integration by parts is a mathematical technique used in the solving of indefinite and definite integrals. The differential functions of the products are expanded and then expressed in the original integrals (Stroud & Dexter, 70).

The single integration by parts begins with the following:

(uv)' = uv' + u'v and integration of both sides of the equation yields; uv = ∫uv' dx + ∫u'v dx

Rearranging the integrals gives;

∫uv' dx = uv − ∫u'v dx

The key concepts required for easy computation of the integration by parts include;

The choice of dx and dx is such a way that; u is easy to differentiate and dx is easy to integrate. In addition, ∫Vdu and ∫udv should be easy to compute. Sometimes in integration by parts, it is necessary to integrate ...

Trigonometric computations are used in nearly all fields of geometry, physics and engineering. The triangulation technique has the great importance, which allows measuring the distance in astronomy and geography, monitoring the satellite navigation system. Also trigonometry is used in such areas as music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medicine and so on. Daniel Bernoulli, Fourier and Cauchy made a huge contribution to the involvement of trigonometry and developed the idea of trigonometric series. In the middle of the XVIII century, appeared the most important in its consequences "argument of a string". Euler ...