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Find the indefinite integral ∫(x^2)*(e^x) dx (Edexcel C4 June 2013 Question 1)

This is an example question where you integrate by parts twice. When answering a question like this it is helpful to memorise general integration formula, so you can quickly and confidently tackle questions ...
DC
Answered by Daniel C. • Maths tutor
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Show that the determinant of the 3x3 matrix (2 1 1 / 2 1 7 / 6 3 5) is equal to zero.

To find the determinant of this matrix, we calculate: 2(1x5-3x7)-1(2x5-6x7)-1(2x3-1x6) = 10 - 42 - 10 + 42 -6 + 6 = 0.So the determinant of this 3x3 matrix is equal to zero.
LG
Answered by LAUREN G. • Maths tutor
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g(x) = ( x / (x+3) ) + ( 3(2x+1) / (x^2 + x - 6) ). Show that this can be simplified to: g(x) = (x+1) / (x-2).

Step 1: The denominator of the right-hand fraction is quadratic, so we can factorise this to (x+3)(x-2). This looks similar to the denominator of the left-hand fraction, suggesting we can combine the two. St...
AS
Answered by Amar S. • Maths tutor
6410 Views

A curve has the equation: x^2(4+y) - 2y^2 = 0 Find an expression for dy/dx in terms of x and y.

First of all expand the brackets in the equation. Then you can differentiate each term with respect to x. As one of the terms will be a product of x and y the product rule must be used to find the differenti...
CM
Answered by Carlotta M. • Maths tutor
4678 Views

Prove that, if 1 + 3x^2 + x^3 < (1+x)^3, then x>0

(1+x)^3 = x^3 + 3x^2 + 3x + 1 (Can be calculated straight away by binomial method or by multiplying brackets individually) if (1+x)^3 &gt; 1 + 3x^2 + x^3then: x^3 + 3x^2 + 3x + 1 &gt; 1 + 3x^2 + x^3 3x &gt; ...
VT
Answered by Vigneswaran T. • Maths tutor
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