三角函數(shù)積分公式是:
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sin(α+β+γ)=sinα·cosβ·cosγ+cosα·sinβ·cosγ+cosα·cosβ·sinγ-sinα·sinβ·sinγ
cos(α+β+γ)=cosα·cosβ·cosγ-cosα·sinβ·sinγ-sinα·cosβ·sinγ-sinα·sinβ·cosγ
tan(α+β+γ)=(tanα+tanβ+tanγ-tanα·tanβ·tanγ)÷(1-tanα·tanβ-tanβ·tanγ-tanγ·tanα)
1、三角函數(shù)積分分為定積分和不定積分。
2、定積分:積分是微積分學(xué)與數(shù)學(xué)分析里的一個(gè)核心概念。通常分為定積分和不定積分兩種。直觀地說(shuō),對(duì)于一個(gè)給定的實(shí)函數(shù)f(x),在區(qū)間[a,b]上的定積分的公式為:f(x)(ab)dx=f(x)(ac)(cb)。
3、不定積分:設(shè)是函數(shù)f(x)的一個(gè)原函數(shù),我們把函數(shù)f(x)的所有原函數(shù)F(x)+C(C為任意常數(shù))叫做函數(shù)f(x)的不定積分,記作,即∫f(x)dx=F(x)+C,其中∫叫做積分號(hào),f(x)叫做被積函數(shù),x叫做積分變量,f(x)dx叫做被積式,C叫做積分常數(shù)。
求解含有三角函數(shù)的定積分c語(yǔ)言程序∫(1+cosπx)dx
#include?stdio.h?
#include?math.h?
#define?PI?(acos(-1))?
#define?STEP?(1e-6)?
double?func(double?x);?
double?inte(double?up,double?down,double?func(double));?
int?main(void)??
{?
double?up,down;?
printf("%lf%lf",up,down);?
printf("%lf\n",inte(1,0,func));?
return?0;?
}?
double?func(double?x)?
{?
return?1+cos(PI*x);?
}?
double?inte(double?up,double?down,double?func(double))?
{?
double?sum;?
for(sum=0;down=up;down+=STEP)?
{?
sum+=func(down)*STEP;?
}?
return?sum;?
}
三角函數(shù)定積分公式是∫sinxdx=-cosx+C等等,積分是微分的逆運(yùn)算,即知道了函數(shù)的導(dǎo)函數(shù),反求原函數(shù),在應(yīng)用上,積分作用不僅如此,它被大量應(yīng)用于求和,通俗的說(shuō)是求曲邊三角形的面積。
三角函數(shù)是基本初等函數(shù)之一,是以角度(數(shù)學(xué)上最常用弧度制)為自變量,角度對(duì)應(yīng)任意角終邊與單位圓交點(diǎn)坐標(biāo)或其比值為因變量的函數(shù)。
你好
ò sin x dx = -cos x + C
ò cos x dx = sin x + C
ò tan x dx = ln |sec x | + C
ò cot x dx = ln |sin x | + C
ò sec x dx = ln |sec x + tan x | + C
ò csc x dx = ln |csc x – cot x | + C
ò sin 2x dx =1/2x -1/4 sin 2x + C
ò cos 2x dx = 1/2+1/4 sin 2x + C
ò tan2x dx =tanx -x+ C
ò cot 2x dx =-cot x-x+ C
ò sec 2x dx =tanx + C
ò csc 2x dx =-cot x+ C
ò arcsin x dx = xarcsin x+√(1-x2)+C
ò arccosx dx = xarccos x-√(1-x2)+C
ò arctan x dx = xarctan x-1/2ln(1+x2)+C
ò arc cot x dx =xarccot x+1/2ln(1+x2)+C
ò arcsec xdx =xarcsec x-ln│x+√(x2-1)│+C
ò arccsc x dx =xarccsc x+ln│x+√(x2-1)│+C
#include?stdio.h
#include?math.h
#define?PI?(acos(-1))
#define?STEP?(1e-6)
double?func(double?x);
double?inte(double?up,double?down,double?func(double));
int?main(void)?
{
double?up,down;
printf("%lf%lf",up,down);
printf("%lf\n",inte(1,0,func));
return?0;
}
double?func(double?x)
{
return?1+cos(PI*x);
}
double?inte(double?up,double?down,double?func(double))
{
double?sum;
for(sum=0;down=up;down+=STEP)
{
sum+=func(down)*STEP;
}
return?sum;
}
文章標(biāo)題:c語(yǔ)言三角函數(shù)的積分,含三角函數(shù)積分
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