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How do I integrate by substitution?

Let's take for example the integral 5x 2 (x 3 -4) 4 dx. This is very difficult and not at all nice to expand in terms of x, so we can effectively "create" a new variable, u, and set it to equal x 3...
EC
Answered by Edward C. • Maths tutor
4032 Views

Is AB perpendicular to BC where A =(2,0,-1), B=(4,3,-6) and C = (9,3,-4)

AB = B - A = (4,3,-6)- (2,0,-1) = (2 , 3 , -5)BC = C - B = (9,3,-4) - (4,3,-6) = (5, 0 , 2) If perpendicular "AB dot BC" should equal zeroAB dot BC = (2,3,-5) dot (5,0,2) = (2x5) + (3x0) + (-5x2) =...
SU
Answered by Syed Usman B. • Maths tutor
4244 Views

How do i use the chain rule twice when differentiating?

Ok so for this question we'll use this example: y = (e -2x^2 + 2) 1/5 We start off by making the expression inside the brackets equal to u. In other words u = e -2x^2 + 2. This also means y = u 1/5 Using the...
IL
Answered by Indiya L. • Maths tutor
5578 Views

∫2x(x+2)^(1/2) dx evaluated from 0->2

First make a substitution so we can apply the power rule ∫x n dx = (x n+1 )/(n+1) + C more simply. Can see u=x+2 means (x+2) 1/2 -> u 1/2 and so will help us apply this rule. Change dx/du=1 implies dx = d...
LP
Answered by Luke P. • Maths tutor
13456 Views

Find the equation of the normal of the curve xy-x^2+xlog(y)=4 at the point (2,1) in the form ax+by+c=0

differentiating: xy'+y-2x+(x/y)y'+log(y)=0rearranging: y'=y(2x-y-log(y))/x(1+y)at (2,1): y'=3/4 so gradient of normal at (2,1) is -4/3so the equation of the normal is y-1=(-4/3)(x-2)which is equivalent to 4x...
SL
Answered by Sam L. • Maths tutor
3511 Views