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Find the value of 2∫1 (6x+1) / (6x2-7x+2) dx, expressing your answer in the form mln(2) + nln(3), where m and n are integers.

This fraction can’t be integrated easily, but if we split it using partial fractions, these will be easier to integrate. To do this, we need to factoise the denominator, as this will follow the method of par...
JM
Answered by Jed M. • Maths tutor
14211 Views

Can you differentiate the following function using two methods:- y = e^(2x+1)

The first method to differentiate this fuction is the basic chain rule method. differentiate 2x+1 and add this to the front of the function. This gives us 2e^(2x+1). the other method to differentiate this fu...
RN
Answered by Rajenth N. • Maths tutor
5773 Views

Core 3 - Modulus: Solve the equation |x-2|=|x+6|.

Modulus , also known as absolute value , takes whatever's between the | straight brackets | and makes it positive. For example, |3|=3, and | - 3|=3. Interestingly, if you have any real number x , then | x |=...
MF
Answered by Michael F. • Maths tutor
32155 Views

Using Trigonometric Identities prove that [(tan^2x)(cosecx)]/sinx=sec^2x

You should begin by identifying all the Trigonometric Identities that may be useful in this problem. Specifically, cosecx=1/sinx tanx=sinx/cosx 1/cosx=secx and possibly tan^2x + 1= sec^2x. I began by changin...
MB
Answered by Mary B. • Maths tutor
9886 Views

Find the equation of the tangent to the curve y=x^3-4x^2+2 at the point (3,-7)

y=x 3 -4x 2 +2A tangent to a curve at a specific point along the line will have excatly the same gradient as the curve at that point. For example if the point was (0,0) the tangent would just be a horizontal...
DW
Answered by Daniel W. • Maths tutor
25041 Views