Differentiate and then integrate: x^2 + 3x

To differentiate, the rule is to bring the power down to the front and multiply the expression, then take one off the value of the power, for example: d/dx(x2) = (2)x2-1 = 2x, so the answer to the the question given is: (2)x2-1 + (1)3x1-1 = 2x + 3
To integrate, you first add one to the power, and then divide the expression by the new value of the power for example: integrate(x2) = x2+1(1/3)So the answer to the question is: x2+1(1/3) + 3x1+1(1/2) = (1/3)x3 + (1/2)x2 + CRemember to add the constant of integration (C) and sometimes if we were to differentiate just a number, the expression would disappear and so we need to account for this in the integral.

Answered by Maths tutor

4882 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve C has the equation y=3x/(9+x^2 ) (a) Find the turning points of the curve C (b) Using the fact that (d^2 y)/(dx^2 )=(6x(x^2-27))/(x^2+9)^3 or otherwise, classify the nature of each turning point of C


Imagine a sector of a circle called AOB. With center O and radius rcm. The angle AOB is R in radians. The area of the sector is 11cm². Given the perimeter of the sector is 4 time the length of the arc AB. Find r.


Water is flowing into a rightcircular cone at the rate r (volume of water per unit time). The cone has radius a, altitude b and the vertex or "tip" is pointing downwards. Find the rate at which the surface is rising when the depth of the water is y.


Given y(x+y)=3 evaluate dy/dx when y=1


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning