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Review for final exam for calculus

Review for final exam for calculus

Summary for calculus exam

Find the moment of inertia of a flat plate covering the region bounded by 𝑦=3π‘₯βˆ’π‘₯2 and 𝑦=π‘₯ with respect to x-axis and y-axis

Find the centroid of the region bounded by the curve 𝑓(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 𝑦=75(𝑒π‘₯150+π‘’βˆ’π‘₯150)
Find the arc length of the cable between the two towers

Consider the region bounded by 𝑓(π‘₯)=π‘’βˆ’π‘₯ 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) ∫(π‘₯3+3)6π‘₯2𝑑π‘₯
b) ∫π‘₯𝑑π‘₯4+π‘₯210
c) ∫π‘₯2sin2π‘₯𝑑π‘₯

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