a) For 0 ≤ x ≤ 1, show thatx^2/√2 ≤ x^2/(√1 + x) ≤ x^2.b) Use the estimate in a) and integrate it to prove that1/3√2 ≤ the integral from 0 to 1 of x^2/(√1 + x) dx ≤ 1/3 .c) By estimating 2x/ sin x on the interval [π/6, π/2], prove that2π^2/9 ≤ integral from π/6 to π/2 of 2x/sin x ≤ 4π^2/9

a) For 0 ≤ x ≤ 1, show thatx^2/√2 ≤ x^2/(√1 + x) ≤ x^2.b) Use the estimate in a) and integrate it to prove that1/3√2 ≤ the integral from 0 to 1 of x^2/(√1 + x) dx ≤ 1/3 .c) By estimating 2x/ sin x on the interval [π/6, π/2], prove that2π^2/9 ≤ integral from π/6 to π/2 of 2x/sin x ≤ 4π^2/9

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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