Find the exact length of the curve. x--L vy dy 3), 4 s y s 16 Need Help? Read it

Question

Find the exact length of the curve. x--L vy dy 3), 4 s y s 16 Need Help? Read it Watch It Chat About It Submit Answer save Progress Practice Another Version 10. O 0/1 points I Previous Answers SCalcET7 8.1.013 Find the exact length of the curve. y n(sec x), 0 SX S T/6 Need Help? Read It Watch It chat About It 11. 0/1 points I Previous Answers SCalcET7 8.1.033 Find the arc length function for the curve y 3/2 with starting point Po( 16, 128 s(x) 253 2) 144 27) x 27 Need Help? Read It Watch It chat About It

Explanation / Answer

f(y)=x=(1/3)y^(3/2) -y^(1/2)

f'(y)=(1/2)y^(1/2) -(1/2)y^(-1/2)

f'(y)=(1/2)(y-1)/y^(1/2)

(f'(y))^2=(1/4)((y-1)^2)/y

arc length=integral[4 to 16] sqrt(1+(f'(y))^2)

integral[4 to 16] sqrt(1+(1/4)((y-1)^2)/y)dy

integral[4 to 16] sqrt(1+ ((y-1)^2)/4y)dy

integral[4 to 16] sqrt( (y/4 +1/4y +1/2))dy

integral[4 to 16] (1/2)sqrt( (y +1/y +2))dy

integral[4 to 16] (1/2)sqrt( (y^2 +1 +2y)/y)dy

integral[4 to 16] (1/2)sqrt( (y+1)^2 /y)dy

integral[4 to 16] (1/2)(y+1)/sqrty dy

integral[4 to 16] (1/2)(sqrty+ 1/sqrty) dy

[4 to 16] (1/2)((2/3)y^(3/2) + 2y^(1/2))+c

[4 to 16] ((1/3)y^(3/2) + y^(1/2))+c

((1/3)16^(3/2) + 16^(1/2)) -((1/3)4^(3/2) + 4^(1/2))

76/3 -14/3

62/3

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.