Question

I don’t know how to do number 10

please with steps and thank you.

Basic Skills 3-6. Setting up arc length integrals Write and simplify, but do not evaluate, an integral with respect to x that gives the length of the fol lowing curves on the given interval. y = In x on [1,10)' y=e-2x On [0.2] 7-16. Arc length calculations Find the arc length of the following curves on the given interval by integrating with respect to x 7, 6, 5, y = 2x + 1 on [ 1,51 (Use calculus.) 8. y 4 3xon-3, 21 (Use calculus.) y =-8x-3 on [-2, 6] (Use calculus.) 9. y=를x3/2 on [0, 601 (x2+2)12 11. y-31n xǐon [1.6] on (4.16 12. x on [1,9 3 4 8r2 T 17-26. Arc length by calculator MacBook Air

Answer 1

Y = 1/ 2(e^x + e^- x) Rightarrow dy/dx = 1/2 (e^x - e^- x) = e^x/2 - e^- x/2 Rightarrow arc lenghth = integral^ln 2_- ln 2 squareroot (1 + (e^2x/4 + e^- 2x/4 - 2e^x - x/4))^1_dx = integral^ln 2_ln 2 squareroot 1 + ex^2 + e^- 2x/4 - 1/2 dx = integral^ln 2_ln 2 squareroot e^2x/4 + e^- 2x/4 + e^x - x dx = integral^ln 2_ln 2 squareroot (e^x + e^- x/2)^2 dx = 1/2 integral^ln 2_ln 2(e^x + e^- x)^dx = 1/2[e^x - e^-x1]^ln2_ln 2 = 1/2 [(2 - e^- ln 2) - (e^- ln 2 - e^ln 2)] = 1/2 [2 - 1/2 -1/2 + 1/2 + 2] = 4 - 1/ 2 = 3/2 arc length = 8/2