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Simplify 125^(-2/3)

Simplify 125 -2/3 A negative indices means that we need to reciprocate the number or "flip it": 125 -2/3 = (1/125) 2/3 A fractional indices can be split up based on the denominator and numerator. H...
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Answered by Bethan H. • Maths tutor
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The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the

formula for volume of solid generated = 2pi x integral between limits of y 2 expand ( e x + 2e -x ) 2 = e 2x +4+4e -2x integrate e 2x +4+4e -2x with respect to x= 1/2(e 2x ) + 4x - 2e -2x (+C) however c won'...
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Answered by Kit T. • Maths tutor
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I’m having some trouble understanding functions. Mainly concerning how to know what the input and outputs are. Could you give me an explanation?

The best way to think about a function is to see it as a machine. Your input is the item you put into the machine, the function is what the machine does, and then when you get out of the other side is your o...
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Answered by Chelsie J. • Maths tutor
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Integrate the function xsin(4x^2) with respect to x, using the integration by substitution method.

Heres our integral: int(xsin(4x 2 )dx)The first decision to make is what to use as our substitution. We're going to go for the term tied up in the sine function: 4x 2 Set u = 4x 2 du/dx = 8x, therefore dx = ...
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Answered by Benjamin C. • Maths tutor
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Find the 1st derivative of y = x^2 + 7x +3 and hence find the curves minima.

Firstly, we differentiate y = x 2 +7x+3 . This gives dy/dx = 2x+7.The minimum value occurs when dy/dx = 0. So find x and y when dy/dx=0. 2x+7=0 implies x= -3.5, which from the first equation means y = (-3.5)...
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Answered by Connor W. • Maths tutor
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