E ^ ( x ) f ( x ) = ∫ (from 0 to x) of sin2tdt పరిష్కరించండి

$$E ^ { ( x ) } f ( x ) = \int _ { 0 } ^ { x } \sin 2 t d t$$

fని పరిష్కరించండి

$$\left\{\begin{matrix}f=\frac{\left(\sin(x)\right)^{2}}{xE^{x}}\text{, }&x\neq 0\text{ and }\left(E>0\text{ or }Denominator(x)\text{bmod}2=1\right)\text{ and }E\neq 0\\f\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{, }n_{1}=0\end{matrix}\right.$$

దీర్ఘాకృతి సమీకరణమును పరిష్కరించడం కోసం దశలు

సమీకరణము ప్రామాణిక రూపంలో ఉంది.

$$xE^{x}f=x\sin(2x)$$

రెండు వైపులా E^{x}xతో భాగించండి.

$$\frac{xE^{x}f}{xE^{x}}=\frac{x\sin(2x)}{xE^{x}}$$

E^{x}xతో భాగించడం ద్వారా E^{x}x యొక్క గుణకారము చర్యరద్దు చేయబడుతుంది.

$$f=\frac{x\sin(2x)}{xE^{x}}$$

E^{x}xతో \sin(2x)xని భాగించండి.

$$f=\frac{\sin(2x)}{E^{x}}$$

Eని పరిష్కరించండి

$$\left\{\begin{matrix}E=\left(\frac{\left(\sin(x)\right)^{2}}{fx}\right)^{\frac{1}{x}}\text{, }&\left(\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(x>\pi n_{2}\text{ and }x<\pi \left(n_{2}+1\right)\right)\text{, }n_{2}>-1\text{ and }f\neq 0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }Numerator(x)\text{bmod}2=1\right)\text{ or }\left(\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{, }not(n_{1}<1)\text{ and }f\neq 0\text{ and }\frac{\left(\sin(x)\right)^{2}}{fx}\geq 0\text{ and }x>0\right)\text{ or }\left(\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{, }not(n_{1}<1)\text{ and }f\neq 0\text{ and }Numerator(x)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x>0\right)\text{ or }\left(\left(\frac{\left(\sin(x)\right)^{2}}{fx}\right)^{\frac{1}{x}}>0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(x>\pi n_{2}\text{ and }x<\pi \left(n_{2}+1\right)\right)\text{, }n_{2}>-1\text{ and }f\neq 0\text{ and }\frac{\left(\sin(x)\right)^{2}}{fx}\geq 0\text{ and }x>0\right)\text{ or }\left(\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }\left(\frac{\left(\sin(x)\right)^{2}}{fx}\right)^{\frac{1}{x}}>0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(x>\pi n_{2}\text{ and }x<\pi \left(n_{2}+1\right)\right)\text{, }n_{2}>-1\text{ and }f\neq 0\text{ and }\frac{\left(\sin(x)\right)^{2}}{fx}\geq 0\right)\text{ or }\left(\left(\frac{\left(\sin(x)\right)^{2}}{fx}\right)^{\frac{1}{x}}<0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(x>\pi n_{2}\text{ and }x<\pi \left(n_{2}+1\right)\right)\text{, }n_{2}>-1\text{ and }f\neq 0\text{ and }\frac{\left(\sin(x)\right)^{2}}{fx}\geq 0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x>0\right)\text{ or }\left(\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }\left(\frac{\left(\sin(x)\right)^{2}}{fx}\right)^{\frac{1}{x}}<0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(x>\pi n_{2}\text{ and }x<\pi \left(n_{2}+1\right)\right)\text{, }n_{2}>-1\text{ and }f\neq 0\text{ and }\frac{\left(\sin(x)\right)^{2}}{fx}\geq 0\text{ and }Denominator(x)\text{bmod}2=1\right)\\E=-\left(\frac{\left(\sin(x)\right)^{2}}{fx}\right)^{\frac{1}{x}}\text{, }&\left(f\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(x>\pi n_{2}\text{ and }x<\pi \left(n_{2}+1\right)\right)\text{ and }x>0\text{ and }\left(\frac{\left(\sin(x)\right)^{2}}{fx}\right)^{\frac{1}{x}}<0\text{ and }\frac{\left(\sin(x)\right)^{2}}{fx}\geq 0\right)\text{ or }\left(f\neq 0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }x=\pi \left(n_{2}+1\right)\text{ and }Numerator(x)\text{bmod}2=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{, }not(n_{1}<1)\text{ and }not(n_{1}=0)\text{ and }x>0\right)\text{ or }\left(\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }f\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(x>\pi n_{2}\text{ and }x<\pi \left(n_{2}+1\right)\right)\text{ and }\left(\frac{\left(\sin(x)\right)^{2}}{fx}\right)^{\frac{1}{x}}<0\text{ and }\frac{\left(\sin(x)\right)^{2}}{fx}\geq 0\right)\text{ or }\left(f\neq 0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(x>\pi n_{2}\text{ and }x<\pi \left(n_{2}+1\right)\right)\text{ and }Numerator(x)\text{bmod}2=1\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }Denominator(x)\text{bmod}2=1\text{ and }Numerator(x)\text{bmod}2=0\right)\text{ or }\left(f\neq 0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(x>\pi n_{2}\text{ and }x<\pi \left(n_{2}+1\right)\right)\text{ and }x>0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }Numerator(x)\text{bmod}2=1\text{ and }Numerator(x)\text{bmod}2=0\right)\text{ or }\left(\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{, }not(n_{1}<1)\text{ and }not(n_{1}=0)\text{ and }f\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Numerator(x)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x>0\right)\\E<0\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }f=0\text{ and }x\neq 0\text{ and }Denominator(x)\text{bmod}2=1\\E=0\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{, }not(n_{1}<1)\text{ and }f=0\\E>0\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }f=0\text{ and }x\neq 0\\E\neq 0\text{, }&x=0\end{matrix}\right.$$