Top answers

Integrate (tanx)^2

Method: We use the trigonometric identity (tanx)^2 +1 = (secx)^2 to understand that (tanx)^2 can be written as (secx)^2-1.We then use the formula booklet to identify that (secx)^2 is a given integral and its...
TD
Answered by Tutor382317 D. • Maths tutor
4628 Views

Given an integral of a function parametrized with respect to an integer index n, prove a given recursive identity and use this to evaluate the integral for a specific value of n.

This exercise is interesting as it combines a variety of concepts fundamental to integration and maths in general. It also allows to introduce the student to the idea of recursion , very often used to solve ...
MC
Answered by Marco C. • Maths tutor
3079 Views

You are given that n is a positive integer. By expressing (x^2n)-1 as a product of factors, prove that (2^2n)-1 is divisible by 3.

X 2n -1 = (x n +1)(x n -1) Therefore we can say 2 2n -1 = (2 n +1)(2 n -1) . As 2 n is always even, a multiple of 3 is always either going to be 1 above or 1 below it, e.g. 3 is one below 4 and 9 is 1 above ...
AL
Answered by Abraham L. • Maths tutor
10153 Views

A circle has equation x^2 + y^2 - 8x - 10y + 5 = 0, find its centre and radius

To find the centre and radius of the circle, you need to get the equation into the form (x - a) 2 + (y - b) 2 = r 2 . You can do this by rearranging to bring the x and y parts together, and completing the sq...
MB
Answered by Martha B. • Maths tutor
8827 Views

The volume of a cone is V = 1/3*pi*r^2*h. Make r the subject of the formula.

Answering the question by acknowledging the student understands what the question is actually asking. The subject of the formula sits by itself on one side of the equation and doesn't appear at all on the ot...
AR
Answered by Alice-Kate R. • Maths tutor
12482 Views