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Hiya! So the very first thing we need to do is find the determinant, which is just a fancy word to describe a matrix; for a 2x2 matrix, it's equal to "ad-bc", where: (a b c d) This will give...

As the derivative of e^x is e^x, so is the integral (plus some constant). As we wish to find the value of the integral from x = 1 to x = 2, we substitute x=2 into e^x, and from that we subtract e^x with x...

x^2+5x+10 -> (x+p)^2+q (x+5/2)^2 - (5/2)^2 + 10 (x+5/2)^2 - (25/4) +40/4 (x+5/2)^2 +15/4

a) When differentiating y, the method with each term is to 'times by the power and minus 1'. In order to apply this, we need every term to consist of a coefficient multiplied by a power of x. To start wit...

Use double angle formula to rearrange for cos2x

this gives: x/2 + 1/4sin2x + C (constant)