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dy/dx = 6x^1/2 + 2 y = (62/3)x^3/2 + 2x + c = 4x^3/2 + 2x + c 38 = (416^3/2) + (2*16) + c c = 38 - 256 - 32 = -250 y = 4x^3/2 + 2x - 250

A tricky question which is actually really simple if you know the technique and will save a lot of time during the exam. The method is to simply add 1 and minus one to the numerator. so the integral becom...

Using the formula for differentiation: if y=ax^N then dy/dx= Na*x^N-1 apply this to each term in the equation given; first term: dy/dx= 9x²second term: dy/dx= 14xth...

A needs to be multiplied up by x+3 to make the fraction have the same in denominator as the other expressions. Then you need to equate the numerators. 3 - 5x = A(x+3) + B
You can gain two simultaneou...

First, we must cross multiply to remove the fractions, to do this, we multiply each numerator by the opposite denominator: (x)(12x+31) = (6x+5)(4x-1). Then, we multiply out the brackets t...