m23 review exercises for long exam 1

# m23 review exercises for long exam 1 - MATH023 Review...

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MATH023 Review Exercises 1. Find the lengths of the following curves: a. g1876=8g1855g1867g1871g2016+8g2016 g1871g1861g1866g2016 , g1877=8g1871g1861g1866g2016−8g2016 g1855g1867g1871g2016 from g2016=0 to g2016= g3095 g2870 b. g1876= g3052 g3120 g2872 + g2869 g2876g3052 g3118 from g1877=1 to g1877=2 . Hint: 1 + (dx/dy) 2 is a perfect square. c. 3 0 , ) ln(cos π = x x y d. 1 0 , 2 cosh 3 2 1 + = x x y e. g1870= g2869 √g2870 g1857 g3087 , 0≤g2016≤g2024 2. Set-up an integral for the length of the following curves and use your calculator to find the curve’s length numerically. a. 0 3 , tan π - = x x y b. 2 / 1 2 / 1 , 1 2 - - = y y x c. ) 3 , 7 ( to ) 1 , 1 ( from 1 2 2 2 - - + = + x y y d. π - = x x x x y 0 , cos sin 3. Set-up an integral for the circumference of the ellipse 3g1876 g2870 +g1877 g2870 =3 . 4. Find the lateral surface area of the cone generated by revolving the line segment g1877= g3051 g2870 , 0≤g1876≤4 about the (a) x -axis and (b) y -axis. 5. Find the area of the surface generated by revolving g1870=4g1871g1861g1866g2016 about the (a) polar axis and (b) 90 o line 6. Set-up an integral for the area of the surface generated by revolving the curve g1876= g2870 g2871 g1872 g2871/g2870 , g1877=2√g1872 , 0≤g1872≤√3

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