Respuesta :

LammettHash
[tex]\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\mathbf f(\mathbf r(t))\cdot\mathrm d(16t^6\,\mathbf i+t^4\,\mathbf j)[/tex]
[tex]=\displaystyle\int_0^1\bigg(16t^{10}\,\mathbf i+6t^8\bigg)\cdot\bigg(96t^5\,\mathbf i+4t^3\,\mathbf j\bigg)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(1536t^{15}+24t^{11})\,\mathrm dt=98[/tex]

The line integral of [tex]\int_{c}f.dr[/tex]  where [tex]r(t)=16t^6i+t^4j[/tex] and [tex]F(x,y)=xyi+6y^2j[/tex]  for [tex]0\leq t \leq 1[/tex] is [tex]98.[/tex]

According to the question,

[tex]r(t)=16t^6i+t^4j[/tex]

[tex]F(x,y)=xyi+6y^2j[/tex]

Now Integrate,

[tex]\int_{c}f.dr=\int_{t=0}^{t=1} f(r(t)).d(16t^6i+t^4j)[/tex]

[tex]=\int_{0}^{1} (16t^6i+t^4j).(96t^5i+4t^3j) dt[/tex]

[tex]=\int_{0}^{1} (1536t^{15}+24t^{11}) dt\\=98[/tex]

Hence, the line integral of [tex]\int_{c}f.dr[/tex]  where [tex]r(t)=16t^6i+t^4j[/tex] and [tex]F(x,y)=xyi+6y^2j[/tex]  for [tex]0\leq t \leq 1[/tex] is [tex]98.[/tex]

Learn more about integration here:

https://brainly.com/question/18125359

Otras preguntas