Question

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Determine whether the following assertions are true or false 1. The double integral JJDy2dA, where D is the disk x2 +y2く1, is equal to π/3 2. The iterated integral J^S 4drdy is equal to 3. The center of mass of the triangular lamina that occupies the region D- 10 4. The triple integral of a function f over the solid tetrahedron with vertices (0,0,0), x < 3,0 < y < 3-2) and has a constant density is at the point (1,1) (1,0,0), (0, 1,0), and (0,0, 1), is equal to ,y 2)dz dydr 5. If (p, θ, φ) denote the spherical coordinates, the equations θ 0, φ-T/3 determine a half-line. 6. The triple integral JJB(a2 + y22)dV, where B is the ball with center the 7. If F is a continuous vector field on the plane and the line integral of F along any 8. If C is the quarter of the circle x2 +y2-1 lying in the first quadrant, the integral origin and radius 2, is 32/5 smooth closed curve is zero, then F is the gradient of some function f. e ry ds is equal to 1/2 the integral ev)da(2r+cos y2)dy is equal to the area of R 9. If R is a rectangle on the plane and C is the positively oriented boundary of R, 10. If F is a vector field in the 3-space and curl F is zero, then div F is zero

Answer 1

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