MATH 0230 Final: MATH 230 m230 Final Exam 5-214
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1 x2 dx: r x+3 x3+x dx. Find the volume of the solid formed when the region bounded by the curves y = x4 + 1, y = 2x2 and the y axis in the rst quadrant is rotated about the x axis. Find the volume of the solid formed when the region which is bounded by the x axis and the curve y = sin(x/2) for 0 x is rotated about the y axis. P = (1, 1, 2): determine the angle between the vectors u and v. Determine the equation of the line tangent to the curve x(t) = cos(2t), y(t) = sin t at the point where t = . Determine the arc length of the curve de ned parametrically by x(t) = et 4t, y(t) = 8et/2, Determine the area inside the shown region which is formed by the polar graph of the polar function r( ) = + 1 for 0 .
