![\boxed{\boxed{ L=\int\limits^a_b { \sqrt{1+[f'(x)]^2} } \, dx }}](/tpl/images/0130/0636/4da38.png)
![L= \frac{4}{81} \int\limits^1_0 { \sqrt{u} } \, dx \\\\\\L= \frac{4}{81} \left[\left( \frac{2u^{ \frac{3}{2} }}{3} \right) \right]^1_0\\\\\\L= \frac{4}{81}* \frac{2}{3} \left[\left( \sqrt{u^3} \right) \right]^1_0\\\\\\\L= \frac{8}{243} \left[ u* \sqrt{u} \right]^1_0\\\\\\L= \frac{8}{243} *\left[ \frac{4+81x}{4} \sqrt{ \frac{4+81x}{4} } \right]^1_0](/tpl/images/0130/0636/b9e96.png)
![L= \frac{8}{243} *\left[ \frac{4+81x}{4} \sqrt{ \frac{4+81x}{4} } \right]^1_0\\\\ L= \frac{8}{243} *\left[ \frac{4+81x}{4} * \frac{ \sqrt{ 4+81x }}{2} \right]^1_0\\\\L= \frac{8}{243}* \frac{1}{4}* \frac{1}{2}*\left[ (4+81x* \sqrt{4+81x} \right]^1_0 \\\\L= \frac{1}{243} \left[\left( 85 \sqrt{85} \right) - \left(4 \sqrt{4} \right) \right]\\\\\\\\\boxed{\boxed{L= \frac{1}{243} \left[85 \sqrt{85}-8 \right]}}](/tpl/images/0130/0636/6d485.png)
![\mathrm{\mathbf{a)}\ y=x^3\ \ \|\ \ {[0,2]}}\\\\ \mathrm{\int\limits_0^2x^3\ dx=\dfrac{x^4}{4}\bigg|_0^2=\dfrac{2^4}{4}-\dfrac{0^4}{4}=\dfrac{16}{4}=\boxed{\mathbf{4\ u.a.}}}](/tpl/images/1075/1488/dc1ea.png)
![\mathrm{\mathbf{b)}\ y=\sin{x}\ \ \|\ \ {[0,\pi]}}\\\\ \mathrm{\int\limits_0^{\pi}\sin{x}\ dx=-\cos{x}\bigg|_0^{\pi}=-\cos{\pi}-(-\cos{0})=}\\\\ \mathrm{=-(-1)+1=1+1=\boxed{\mathbf{2\ u.a.}}}](/tpl/images/1075/1488/6058a.png)
![\mathrm{\mathbf{c)}\ y=\cos^2{x}\ \ \| \ \ {[0,\frac{\pi}{2}]}}\\\\ \mathrm{\int\limits_0^{\frac{\pi}{2}}\cos^2{x}\ dx=\int\limits_0^{\frac{\pi}{2}}\dfrac{1+\cos{2x}}{2}\ dx=}\\\\ \mathrm{=\dfrac{1}{2}\bigg(\int1\ dx+\int\cos{2x}\ dx\bigg)\bigg|_0^{\frac{\pi}{2}}=}\\\\ \mathrm{=\dfrac{1}{2}\bigg(x+\int\cos{2x}\ dx\bigg)\bigg|_0^{\frac{\pi}{2}}\dots}](/tpl/images/1075/1488/46d5c.png)
.
:
Seja a função f. Determine a área da curva sobre o intervalo [0, 1]
f (x) = √5x + 4
...
Matemática, 11.12.2020 07:20 aryanemendes2602
Seja a função f. Determine a área da curva sobre o intervalo [0, 1]
f (x) = √5x + 4
Respostas: 3
Outra pergunta: Matemática
Matemática, 15.08.2019 01:04
Divida o numero 1080 em partes diretamente proporcionais a 1/2 e 3/4 e inversamente proporcionais a 5 e 6 ao mesmo tempo
Respostas: 1
Matemática, 15.08.2019 00:11
No lançamento de dois dados qual a probabilidade de sair dois números pares? números divisíveis por três
Respostas: 3
Você sabe a resposta certa?
Perguntas
Matemática, 25.05.2021 07:00
Geografia, 25.05.2021 07:00
Geografia, 25.05.2021 07:00
Sociologia, 25.05.2021 07:00
Matemática, 25.05.2021 07:00
Matemática, 25.05.2021 07:00
Matemática, 25.05.2021 07:00
Sociologia, 25.05.2021 07:00
