Physics equations/07-Work and Energy/Q:lineIntegral

Integrate the line integral of, ${\displaystyle {\vec {F}}=9xy{\hat {x}}+9.5y^{3}{\hat {y}}}$, along the y axis from y = 5 to y = 14

Integrate the function, ${\displaystyle {\vec {F}}=r^{7}\theta ^{9}{\hat {r}}+r^{7}\theta ^{5}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 8

Integrate the line integral of ${\displaystyle {\vec {F}}=4xy{\hat {x}}+7.7x{\hat {y}}}$ from the origin to the point at x = 2.5 and y = 3.3

Integrate the function, ${\displaystyle {\vec {F}}=-x^{2}y^{2}{\hat {x}}+x^{2}y^{3}{\hat {y}}}$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1)}. Orient the path so its direction is out of the paper by the right hand rule

Integrate the line integral of, ${\displaystyle {\vec {F}}=7.8xy{\hat {x}}+9.6y^{3}{\hat {y}}}$, along the y axis from y = 6 to y = 16

Integrate the function, ${\displaystyle {\vec {F}}=r^{8}\theta ^{9}{\hat {r}}+r^{9}\theta ^{3}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 9

Integrate the line integral of ${\displaystyle {\vec {F}}=2.9xy{\hat {x}}+9.9x{\hat {y}}}$ from the origin to the point at x = 2.5 and y = 3.5

Integrate the function, ${\displaystyle {\vec {F}}=-x^{5}y^{2}{\hat {x}}+x^{3}y^{5}{\hat {y}}}$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1)}. Orient the path so its direction is out of the paper by the right hand rule

Integrate the line integral of, ${\displaystyle {\vec {F}}=6.3xy{\hat {x}}+8.3y^{3}{\hat {y}}}$, along the y axis from y = 3 to y = 16

Integrate the function, ${\displaystyle {\vec {F}}=r^{7}\theta ^{8}{\hat {r}}+r^{9}\theta ^{9}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 8

Integrate the line integral of ${\displaystyle {\vec {F}}=2.9xy{\hat {x}}+9.6x{\hat {y}}}$ from the origin to the point at x = 2.6 and y = 3.1

Integrate the function, ${\displaystyle {\vec {F}}=-x^{2}y^{5}{\hat {x}}+x^{3}y^{5}{\hat {y}}}$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1)}. Orient the path so its direction is out of the paper by the right hand rule