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Explain how integration via substitution works.

The function in terms of x should be broken down into two easier to integrate functions, like so f(x) = g(h(x)). if we say that u=h(x) is our substitution then we can integrate in terms of u now, however the...
DF
Answered by Daniel F. • Maths tutor
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Express 6sin(2x)+5cos(x) in the form Rsin(x+a) (0degrees<x<90degrees)

Expand sin(2x) to 2sin(x)cos(x) so you have 6(2sin(x)cos(x))sec(x). cos(x) and sec(x) cancel out so the expression becomes 12sin(x) + 5cos(x). compare this to the expanded version of Rsin(x+a) which is Rsin(...
JR
Answered by Jacob R. • Maths tutor
5395 Views

3/5 of a number is 162. Work out the number.

Something multiply 3/5 = 162Think of this something as a piece of cake. Now this cake has been equally sliced into 5 pieces. 3 pieces of the cake is worth 162 (let's give it a value, pound, dollar, or anythi...
HK
Answered by Han K. • Maths tutor
4516 Views

If a curve has equation y = (-8/3)x^3 - 2x^2 + 4x + 18, find the two x coordinates of the stationary points of this curve.

The first step in solving this question is to differentiate equation y with respect to x. To differentiate a given 'x' term in an equation use the following method --&gt; x n becomes nx (n-1) .y = (-8/3)x 3 ...
RT
Answered by Robyn T. • Maths tutor
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A curve has equation y=x^2 + 2x +5. Find the coordinates of the point at which the gradient is equal to 1.

dy/dx= 2x+2 , gradient is equal to 1 so dy/dx also equals 1.1=2x+2-1=2xx=-1/2plug this value of x into the equation to get y=17/4
NL
Answered by Nikhil L. • Maths tutor
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