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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 value(s) of x which satisfies the equation 3x^2 + 6x + 3 = 0

First we must multiply the coefficient of x2 by the value with no x associated with it3x3 = 9Now we must find two numbers that add to make 6 and multiply to make 9+6x9 3 and 3Now we need to split the coef...

Answered by Jacob G. • Maths tutor

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The line L1 is given by the Equation y =3x+5, and the line L2 is given by the Equation 4y-12x+16=0. Show that the lines L1 and L2 are Parallel

Rewrite the equation for L2 to find an equation for y4y=12x-16; y = 3x - 4 2. The x-coefficient gives the gradient (or slope) of the line, so since the gradient of L1 is 3, and as we have just shown, the ...

Answered by William S. • Maths tutor

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Solve the simultaneous equations for x and y: 3x+3y=5 and 6x+5y=9

3x+3y=5 6x+5y=9Multiply the first equation by 2 to get a workable x coefficient:6x+6y=10Write the equations above each other and subtract them:6x+6y=10 ...

Answered by Joe C. • Maths tutor

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