What is the formula for calculating reduction?

Reduction Formula for Trigonometric Functions

\int sin^{n}(x)dx=\frac{-Sin^{n-1}(x)Cos(x)}{n}+\frac{n-1}{n}Sin^{n-2}(x)dx.
\int tan^{n}(x)dx=\frac{-tan^{n-1}(x)}{n-1}-\int tan^{n-2}(x)dx.
\int sin^{n}(x)\: cos^{m}(x)dx=\frac{sin^{n+1}(x)cos^{m-1}(x)}{n+m}+\frac{m-1}{n+m}\: \int sin^{n}(x)\: cos^{m-2}(x)dx.

What is the use of reduction formula in integration?

A reduction formula is one that enables us to solve an integral problem by reducing it to a problem of solving an easier integral problem, and then reducing that to the problem of solving an easier problem, and so on.

What is the formula for integrals?

Derivation of the formula for integration by parts dx = d(uv) dx = u dv dx + v du dx . Rearranging this rule: u dv dx = d(uv) dx − v du dx . Now integrate both sides: ∫ udvdx dx = ∫ d(uv) dxdx − ∫ v du dx dx.

What is reduction formula in trigonometry?

For convenience, we assume θ is an acute angle (0°<θ<90°). When determining function values of (180°±θ), (360°±θ) and (−θ) the function does not change….Co-functions.

second quadrant (180°−θ) or (90°+θ)	first quadrant (θ) or (90°−θ)
sin(90°+θ)=+cosθ	tan(360°+θ)=tanθ
cos(90°+θ)=−sinθ	sin(90°−θ)=cosθ
	cos(90°−θ)=sinθ

What is the integral of 2?

2x + c
So the integral of 2 is 2x + c, where c is a constant. A “S” shaped symbol is used to mean the integral of, and dx is written at the end of the terms to be integrated, meaning “with respect to x”. This is the same “dx” that appears in dy/dx .

What is the integral of Sec 2?

Math2.org Math Tables: Table of Integrals

cos x dx = sin x + C Proof	csc x cot x dx = – csc x + C Proof
sin x dx = -cos x + C Proof	sec x tan x dx = sec x + C Proof
sec2 x dx = tan x + C Proof	csc2 x dx = – cot x + C Proof