area by integration

The moment of inertia bounded by y=x^3 , y=2x , X + y= 6, with respect to x=2 pa help po until Friday. Plus ask ko Lang po ang pinakakapakipakinabang na calculus book for integration applications. Thanks.

plane areas

Find the area bounded by the curve y = ln x/x, the x-axis and the maximum ordinate.

ans. 1/2

1)An excavation is 12 ft. deep and has trapezoidal sides (faces). The upper base is horizontal rectangle 400 ft. by 180 ft., and the lower base is a horizontal rectangle 350 ft. by 150 ft. How many cubic yards of earth were removed in digging the excavation?

2)A chimney in the shape of a frustum of a regular pyramid is 186.3 ft. high. Its upper base is a square 10 ft. on a side, and its lower base is a square 16 ft. on a side. The flue is of uniform square cross section. 7 ¼ by 7 ¼ ft. find the weight of the chimney if the material weighs 112.8 lb. per cu. ft.