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Using a suitable substitution, or otherwise, find the integral of [x/((7+2*(x^2))^2)].

The point of using a substitution when dealing with integrals is to reduce the problem from a very complicated integral to a simplistic one. How can we achieve this with our integral? Well, we know that when...
GF
Answered by George F. • Maths tutor
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The polynomial f(x) is defined by f(x) = 18x^3 + 3x^2 + 28x + 12. Use the Factor Theorem to show that (3x+2) is a factor of f(x).

The factor theorem states that if (x+a) is a factor of f(x), then f(-a)=0. This basically means that if (x+a) is a factor of f(x), then when (x+a)=0, f(x)=0, i.e. when x=-a, f(-a)=0. Our (x+a) in this case i...
GF
Answered by George F. • Maths tutor
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Use simultaneous equations to find the points where the following lines cross: 3x - y = 4 and x^2 + 7y = 5

The points where the lines cross are the points where the two equations equal each other. To do this we solve simultaneous equations. Call equations as follows:(a) 3x - y = 4(b) x 2 + 7y = 5 First take (a) a...
EM
Answered by Emma M. • Maths tutor
3847 Views

Differentiate 4(x^3) + 3x + 2 with respect to x

Solution: 12x 2 + 3 Working: General differentiation formular: d/dx (ax n ) = an(x n-1 ) So we multiply the coefficient (constant infront) of the x term by the power of x (in this case: n) and reduce the pow...
TD
Answered by Tutor77028 D. • Maths tutor
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Find the acute angle between the two lines... l1: r = (4, 28, 4) + λ(-1, -5, 1), l2: r = (5, 3, 1) + μ(3, 0, -4)

To do this, we will only consider the direction vectors of each line. That is to say, the vector 'attached' to our λ and μ terms (which are called scalar parameters).We will do this because the angle between...
RB
Answered by Rory B. • Maths tutor
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