SOLVED: In the following problem, we will use integration by parts to evaluate the indefinite integral of sin x dx.Part 1:How should we choose u and dv?Hint: We can write the integral as ∫ sin x dx, in which case du = dx and dv = sin x dx.Part 2:Use the integration by parts formula to rewrite the integral ∫ sin^-1 x dx.Part 3:Finally, evaluate the indefinite integral ∫ sin x dx.Your answer here should contain an arbitrary constant.Note: You can earn partial credit on this problem.

SOLVED: 49-54 Use the Comparison Theorem to determine whether the integral is convergent or divergent: 1 sin x 49. dx 50. x3 1 dxx 1 dx Vx4 sec?x dx Xvxarctan x dx 2 ex51.52.sin?x dx Vx53.54.

SOLVED:Verify if the vector field F (1223 3ye*y 2, -6y2 3xe*y, .) is conservative and evaluate the line integralJc F . dRwhere C is the curve parameterized by R = for 0 < t < 4r_AI=1B.[ = 3C[ =4D.[ =00 &I =-4n