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Question Number 26584 by gunawan last updated on 27/Dec/17

$${\int }_a^x{(x-t)}^{5}y\left(t\right)dt=4x^6$$$$y\left(x\right)=...$$

Commented by prakash jain last updated on 27/Dec/17

$$\frac{d}{dx}{\int }_{a\left(x\right)}^{b\left(x\right)}f(x,t)dt$$$$=f(x,b\left(x\right))\frac{d}{dx}b\left(x\right)-f(x,a\left(x\right))\frac{d}{dx}a\left(x\right)+$$$${\int }_{a\left(x\right)}^{b\left(x\right)}\frac{\partial }{\partial x}f(x,t)dt$$$$\frac{d}{dx}a\left(x\right)=0$$$$f(x,x)=0$$$$4\cdot 6\cdot x^5={\int }_a^{x}5{(x-t)}^{4}y\left(t\right)dt$$$$4\cdot 6\cdot 5\cdot x^4={\int }_a^{x}5\cdot 4{(x-t)}^{3}y\left(t\right)dt$$$$continuetoget$$$$24x={\int }_a^{x}y\left(t\right)dt$$

Commented by prakash jain last updated on 27/Dec/17

$$\mathrm{Do}\mathrm{you}\mathrm{have}\mathrm{the}\mathrm{final}\mathrm{answer}?$$$$\mathrm{i}\mathrm{am}\mathrm{not}\mathrm{able}\mathrm{to}\mathrm{get}\mathrm{to}\mathrm{a}\mathrm{final}\mathrm{answer}.$$

Commented by prakash jain last updated on 27/Dec/17

$$F\left(x\right)={\int }_a^x{(x-t)}^{5}y\left(t\right)dt=4x^6$$$$F\left(a\right)={\int }_a^a{(a-t)}^{5}y\left(t\right)dt=0$$$$\Rightarrow 4a^6=0\Rightarrow a=0$$$$canyoupleasecheckquestion$$$$ifa=0,y=24$$

Commented by prakash jain last updated on 28/Dec/17

$$\mathrm{Integrate}\mathrm{after}\mathrm{puttimg}y=24.$$$$\mathrm{Also}\mathrm{value}\mathrm{of}a\mathrm{can}\mathrm{only}\mathrm{be}0.\mathrm{Since}$$$$\mathrm{F}\left(a\right)=0.$$

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