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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(4x²)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: 4x²Set u = 4x²

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 = x²+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 mean...

Answered by Connor W. • Maths tutor

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Find the coordinates of the point of intersection between the line L:(-i+j-5k)+v(i+j+2k) and the plane π: r.(i+2j+3k)=4.

By inspection we can tell that the line and the plane are not parallel. Since the dot product between the direction vector of the line with the perpendicular vector of the plane was not equal to 0 (i.e. b...

Answered by Liam V. • Maths tutor

3121 Views

How do I implicitly differentiate and why does it work? (Assuming understanding of differentiation)

Implicit differentiation can be used when you are asked to find dy/dx of a function that has not been written as y=f(x) e.g. y = x^2 - 1, and which cannot be rearranged as such. We can use the equation of...

Answered by Sorcha O. • Maths tutor

3172 Views

Find dy/dx when y = (3x - 1)^10

The question is asking us to find the first derivative of the function (y) with respect to x terms.y = (3x -1)^10We start by taking the superscript 10 down to the front, and multiply this by the 3 (as per...

Answered by Olivia F. • Maths tutor

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