Question

Find the mass of a wire in the shape of a straight line from the point (?3, −1?) to the point (?4,2)? (in cm) if the density is given by p(??x, y)=? ? x^2y (in g / cm).

Answer 1

Remarcko If eay is the mass density of Spey) ds - Spe), 9 (0) 8-10.3+(913 a wire, then mass 2 dt VI ty B(4,2) Now, the equation of the straight line through the points A (3,-) and B(4,2) is passing x A(3,-) ht 2+1 4-3 we Y+ 1 =362-3) y = = 3x - 10 Now, consider the parametric equation of the straight line X(t)=t, y(t) = 30 -0. then (as & is from 3 to 4 35+34" as

Now density function Pa = x²y px (t), y(t)) = ť? (34-10) form above mentioned formula, we get Sprends mass = S p (RCA), 8 (4) 사 t=3 p(x (4), y(4) J (45)('()2 Cos x'(t=1 = + (3 +-10) / 18+ 3² at t=3 4 3. 4 (3 t3 - 10 t) at 4 = vo for etto Tg69_n 3,64 3 = Jio 3x 64 - 10x64 10X64 - 181 + 10% a 10] - To x 95 12 25.035 so, the mass of the wire is (25.035 g