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Using the substitution x = 2cosu, find the integral of dx/((x^2)(4-x^2)^1/2), evaluated between x=1 and x=sqrt(2).

Starting with x=2cosu, rearrange for u to get u=arccos(x/2), then find the upper and lower limits of the integral. We find that our lower limit goes from 1 to pi/3, ad our upper limit goes from root 2 to pi/...
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Calculate the integral of e^x*sin x

1/2 *e^(x)(sin x -cos x)
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Find the equation of the tangent to curve y=5x^2-2x+3 at the point x=0

y=5x 2 -2x+3 Differentiate to find the equation of the gradient of the curve dy/dx=10x-2 Substitute x=0 to find the gradient at the point x=0 dy/dx=-2 y=5 0^2-2 0+3 Substitute x=0 into the original equation ...
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Solve the equation 2x^3 - 5x^2 - 4x + 3 = 0.

In order to answer this question, the expression on the left side of the equation needs to be factorised. This can be done in three stages. 1) finding a factor by subbing in common integers (0, +/- 1, +/-2, ...
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Core 3 Differentiation: If y = (3x^2 + 2x + 5)^10, find its derivative, dy/dx. Hint: Use the chain rule.

The function y = (3x 2 +2x+5) 10 is an example of a "function within a function", which means the thing in the brackets is a function itself, and it's being raised to the power of 10. This is a str...
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