Summary for calculus exam
Find the moment of inertia of a flat plate covering the region bounded by π¦=3π₯βπ₯2 and π¦=π₯ with respect to x-axis and y-axis
Find the centroid of the region bounded by the curve π(π₯)=cosπ₯ and the x-axis and the y-axis in the first quadrant.
An electric cable is hung between two towers that are 200 feet apart as shown in the diagram. The cable takes the shape of a catenary arch whose equation is π¦=75(ππ₯150+πβπ₯150)
Find the arc length of the cable between the two towers
Consider the region bounded by π(π₯)=πβπ₯ and π₯=ln2 in the first quadrant. If this region is rotated by the y-axis, what volume will be generated?
5) Evaluate each integral. Do not use the integral table
a) β«(π₯3+3)6π₯2ππ₯
b) β«π₯ππ₯4+π₯210
c) β«π₯2sin2π₯ππ₯
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