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when integrating you must add one to the power and divide by the new power. so y=(5x^(2 + 1))/3 + (x^(1+1))/2 + 2x + c now substitute 1 for x and 3 for y so 3= (5(1)^(2 + 1))/3 + ((1)^(1+1))/2 + 2(1) +...

The key to answering this question is to recognise that a common substitution of u=sin(x) wont work straight away so we must write the integral in a different form. Knowing that cos(2x)=1-2sin^2(x), the s...

1/4sin(2x) + x/2 + c

y=e^x When we derive, the power is brought down to the front - e.g. 2e^2x. Once this has been reached, you must normally remember to reduce the power by 1. However, with the exponentials, the power remain...

Rearrange to get x^2 - 9x - 36 <= 0 Solve quadratic (x-12)(x+3) <= 0 Solve for x x = 12, x = -3

Now, we have key points 12 and -3, we need the range of values for x where x^2 - 9x - 36 &...