Question

Hey, I need some calc help

Answer 1

k

Answer 2

any and all help is appreciated!!!!!

Answer 3

For the first one, C is just the arbitrary constant--but it's not standard. I prefer to use k for my constants. a and b are your limits of integration--it's based off of Riemann sums.

For the second one, recall that a differential is just d("whatever"). So we want to solve for the differential y, given that y=g(x). If you did the derivative of this, it would be dy/dx=g'(x). Multiply both sides by dx to get dy=g'(x)dx

We don't use the chainrule for this because g(x) implies that it's not a compound function.

The third one is either A or B--it's part of the fundamental theorem of calculus and most textbooks call the same one the "first" but I'm not sure that it's standard. Even if it is, I don't think it should be. I'll call whichever part I want to whatever I want to. Refer to your textbook/notes for this--basically, it's the part of the fundamental theorem of calculus that talks about taking the derivative of a definite integral; which is just the integrand evaluated at the upper limit of integration(assuming the lower end is a constant) times the derivative of the upper limit of integration(which is usually just 1)