Find the mass of the two-dimensional object. A disk of radius 8 with a density function ρ(x)=10x where x is the distance from the point to the origin. Round your answer to two decimal places.

Find the arclength of y=3×2+3 on 0≤x≤1. Round your answer to three decimal places.

The doubly charged ion N2+ is formed by removing two electrons from a nitrogen atom. What is its ground-state electron? [Ans1] Estimate the energy (in eV) of the least strongly bound level in its L shell? [Ans2]

∫ 7xe4xdx =

Find the word done for a force F=36×2 N from x=1 to x=6 m. Round your answer to the nearest whole number.

Evaluate ∫-ππcos2(7x)dx. Round your answer to four decimal places.

Solve the following initial value problem: If dydt=5t and y(0)=-6, then y= ________________

Find the partial fraction decomposition of ∫11×2-13x+10(x2+5)(x-3)dx

Suppose that R is the finite region bounded by y=x, y=x+1, x=0, and x=5. Round your answer to four decimal places.

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