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Before we blindly start using the integration by parts formula, we can see that no matter how many times we differentiate or integrate sin(x) we will still have a trigonometric function. The aim of the 'b...

5 x(3+2) =5x(5)= 25

Rearrange one of the equations to make y the subject:y = 5 - 2x Substitute y into the other equation: 3x + 5 - 2x = 7 x = 2 y = 5 - (2 x 2) y = 1

When integrating, we raise the power by 1 and divide by the new powerSo, 2x⁵ becomes 2x⁶ /6 which simplified down as the question asks is x^6/3-1/(4x³) is -(1/4)x^^-3<...

12 items of fruit. 4/12 are apples - can 4/12 be simplified? Yes both can be divided by 4 and so the fraction becomes = 1/3 for the probability of taking an apple.
The probability of NOT taking an ap...