21b_ps5 - b) find its volume 5) Use the Disc Method to...

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Co-21B Problem Solving #5T 1) Find the area of the “triangular” region bounded on the left by x + y = 2 , on the right by y = x 2 , and above by y = 2 2) Region R is bounded by y = x 2 and y = 3 x . SET UP integrals that could be used to find the volume of the solid formed if R is revolved about: a) the x –axis b) the y -axis c) y = ! 4 d) x = 3 3) The base of a solid is a circle with radius 4. Find the volume of the solid if cross-sections taken perpendicular to the base are: a) squares b) equilateral triangles c) semi-circles 4) A lumberjack saws a wedge out of a cylindrical tree of radius 2 ft . The first cut is parallel to the ground and stops at the axis (center) of the tree. The second cut makes an angle of 45 ! with the first cut and meets it along a diameter. a) carefully sketch the wedge
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Unformatted text preview: b) find its volume 5) Use the Disc Method to verify the volume of a cone = 1 3 ! r 2 h 6) A water tank shaped like a hemisphere with radius 10 ft is filled with water to a depth of 6 ft. Find the volume of water in the tank. 7) A cylindrical glass of height 12 in and radius 2 in , full of water, is tilted until the remaining water just covers the circular base. Calculate the volume of water left in the glass using: a) rectangular cross-sections b) common sense 8. More practice with integration a) x 3 x 4 + 1 dx ! b) x 4 + 1 x 3 dx ! c) x 7 ( x 4 + 1) 3 dx ! d) e x ( x + 1)sin( xe x ) dx ! e) cos(5 x ) 1 + sin(5 x ) dx ! f) cos(4 x ) 1 + sin 2 (4 x ) dx ! [hint: use a trig identity] g) sin(3 x ) 1 ! sin 2 (3 x ) dx " h) (sin2 x + cos2 x ) 2 dx !...
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