discover the range integral over the road C shown in figure regarding right. Integrate(x^2+y^2)dy the worth for the range integral is . (kind an integer or a simplified small fraction.)

Look at the range integral: J( +y’d. Right here, the trail C is made of two-line portions from (0,0) to (1,0), and from (10) towards road of integration is sketched as shown in figure below (0,0) therefore, separated the trail of integration into two components, G and C2 . On G, the range part from (0,0) to (10) is yo allow x = t, y-0 and t differs from 0 to at least one . Right here, dy =0, as 1,-0.

On C2, the range part from (1,0) to (1,1) is x=1. Allow x=1, y-r and t differs from 0 to l. Right here, dv=dt, asy-r. The range integral will likely be =0+ 1 (1+t’)dt 0 4 4 for that reason, the worth for the range integral is, j(x+y*)dy