108Fall12Ex1VersionASolutions

All limits of integration should be expressed as

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Unformatted text preview: 2 Which of the following integrals gives the volume of the solid whose base is 13. 1 (3 pts.) bounded by y = − x + 1 and the x and y axes and whose cross sections, taken 2 perpendicular to the base and parallel to the y- axis, are semicircles? 2 2 1 1 ⎡1 ⎛ 1 ⎞⎤ a) *** ∫ π ⎢ ⎜ − x + 1⎟ ⎥ dx ⎝2 ⎠⎦ 2 ⎣2 0 2 2 ⎛1 ⎞ c) ∫ π ⎜ − x + 1⎟ dx ⎝2 ⎠ 0 2 b) 1 ⎡1 ⎤ ∫ 2 π ⎢ 2 ( 2( y − 1))⎥ dy ⎣ ⎦ 0 1 d) ⎣ ⎦ ∫ π ⎡ −2 ( y − 1)⎤ 2 dy 0 14. (3 pts.) Simplify the expression sin tan −1 ( 3x ) . ( c) *** 3x 1 + 9x2 1 b) 1 − 9 x 2 a) ) 1 + 9x2 3x d) 1 − 9x2 15. (3 pts.) Which integral represents the arc length of the curve y = − ln x on the interval 1 ≤ x ≤ e−2 ? e−2 a) ∫ 1 − x −2 dx 1 b) *** ∫ 1 +...
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