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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 questio...

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.

Answered by LAUREN G. • Maths tutor

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Given that y is directly proportional to square root of x and that y = 20 when x = 49 find an expression to represent x and y.

y = k √x20 = k √49 20/7 = ktherefore y = 20/7 √x

Answered by Ann P. • Maths tutor

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Two ordinary fair dice are rolled. Work out the probability that both land on a value less than 4.

The probability of an event= Number of ways an event can occur/ Total number of possible outcomesBoth dices land on values less than 4. This means they both can be 1,2 or 3. Therefore, number of ways the ...

Answered by George S. • 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, suggesti...

Answered by Amar S. • Maths tutor

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