Find, w.r.t to x, both the derivative and integral of y=6*sqrt(x)
Understand the question:
'w.r.t' stand for 'with respect to', so the qestions is asking for the dericative and integral to be calcuated in terms of x - so find dy/dx and (integral sign) y dx.
Sqrt(x) is the same as x1/2
Deriative
Bring power to the front and decrease the power by one: dy/dx = 61/2x(1/2)-1 = 3x-1/2
Integral
Increase the power by one and divide by the new power: I = 6/((1/2)+1)*x(1/2)+1 = 4x3/2 + C
IF YOU ARE DOING A DEFINATE INTEGRAL (ONE WITHOUT LIMITS) NEVER FORGET TO PUT + C (PLUS CONSTANT. This is a very easy way to drop a mark.
JR
Related Maths A Level answers
All answers ▸Use integration by parts to find ∫ (x^2)sin(x) dx. (A good example of having to use the by parts formula twice.)
A curve has equation 3x^4/3-16y^3/4=32. By differentiating implicitly find dy/dx in terms of x and y. Hence find the gradient of the curve at the point (8,1).
Integrate 3x^2+cos(x) with respect to x
Given the two curves y1 and y2, verify the two curves intersect at (-5,0) and (2,0)