Answer the following word problems about antidifferentiation and definite integrals. Provide a complete solution. Thanks.

I. Antiderivatives. Evaluate the following. t- -3t7+18 1. dt 6 2. J (4-5x) 10 dx sec2 3. x. tan X. dx Il. Definite Integrals and Applications. 1. Find the area of the region bounded by the x-axis and the curve y = x4 - 8x3 + 18x2 - 24. 2. Sketch and set up the integrals find the area of the region bounded by the curves below using both horizontal and vertical strips (two solutions): y=3-x, y=1-1-(x-1)2, y=1-1 -(x+1)2 3. Find the length of the curve 6xy = y# + 3 over the interval y e [1,2]