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Solve 2sin2θ = 1 + cos2θ for 0° ≤ θ ≤ 180°

sin2θ = 2sinθcosθ (double angle formula for sine)cos2θ = cos 2 θ - sin 2 θ (double angle formula for cosine) = 2cos 2 θ - 1 (utilising the trignometric identity sin 2 θ + cos 2 θ = 1) We substitute these int...
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Answered by Samuel N. • Maths tutor
13622 Views

Integrate the function f(x) = 1/(4x-1)

t Using the fact that d/dx ( ln g(x)) = g'(x)/g(x), we can see that the integral of this function will be an ln function. From observing f(x) we see that if the answer was ln(4x-1) then f(x) would need to be...
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Answered by Sachin V. • Maths tutor
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How do I integrate 4x*exp(x^2 - 1) with respect to x?

During the session I would go step by step through the integration by substitution.
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Answered by Anmol S. • Maths tutor
3883 Views

Integrate (1 - x^2)^(-0.5)dx within the limits 0 and 1

The answer is π/2. The key trick to solving this problem is to change variables by using the substitution x = sin(θ). We then need to change the differential and the limits too.
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Answered by Cameron W. • Maths tutor
4299 Views

Differentiate y = x^3− 5x^2 + 3x

the rule for differentiating in terms of x is to multiply by the power then decrease the power by one. So going through the equation x^3 will be multiplied by 3 and go to x^2 so will be 3x^2. Then its import...
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Answered by Georgia D. • Maths tutor
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