Math 215: Final Exam 2024 with 100% correct answers

what is the equation for finding the mass of a function on a line integral? correct answersm=∫a→b p[x(t),y(t),z(t)]∙[x'(t)²+y'(t)²+z'(t)²]^(1/2) dt how do you find moment about the x-axis correct answersMyz=∫a→b x∙p(x,y,z) ds NOTE: the x/y/z in p(x,y,z) gets parameterized to t before solving. use t limits to solve how do you find moment about the y-axis correct answersMxz=∫a→b y∙p(x,y,z) ds NOTE: the x/y/z in p(x,y,z) gets parameterized to t before solving. use t limits to solve how do you find moment about the z-axis correct answersMxy=∫a→b z∙p(x,y,z) ds NOTE: the x/y/z in p(x,y,z) gets parameterized to t before solving. use t limits to solve line integral of f over C wrt arc length (when f is constant function) correct answers∫c f(x,y)ds = ∫a→b f[x(t),y(t)]∙[x'(t)²+y'(t)²]^(1/2) dt 3D line integral of f over C wrt arc length correct answers∫c f(x,y,z)ds = ∫a→b f[x(t),y(t),z(t)]∙[x'(t)²+y'(t)²+z'(t)²]^(1/2) dt integrals for work correct answers∫c (F*T)ds a function on C. T= unit tangent vector ∫c (F*T)ds is equal to? correct answers∫c F(r(t))*r'(t) dt