Why is ꭍ2x=x^2+C?

Differentiating x2 gives dx2/dx=2x. Differentiating a constant C gives 0. d( x2 +C)/dx=dx2/dx+dC/dx=2x+0=2x. Since integration is the inverse function of differentiation, integrating 2x gives x2+C.

LD

Related Maths A Level answers

All answers ▸

The region R is bounded by the curve y=sqrt(x)+5/sqrt(x) the x-axis and the lines x = 3, x = 4. Find the volume generated when R is rotated through four right-angles about the x-axis. Give your answer correct to the nearest integer.


If a ball is dropped from 6m above the ground, how long does it take to hit the floor and what is its speed at impact (assuming air resistance is negligible)?


How do we know that the derivative of x^2 is 2x?


Find dy/dx for y=5x^3−2x^2+7x−15