Top answers

Solve the integral int(sin^2(x))dx

Knowing that 1-2sin 2 (x) = cos(2x), substitute sin 2 (x) as: sin 2 (x) = (1-cos(2x))/2Use the linearity of the integral to split it into: Int(1/2) - Int(cos(2x)/2)dxWhich is in the end:0.5x - 0.25 sin(2x) +...
MM
Answered by Maks M. • Maths tutor
1736 Views

Solve the simultaneous equations x^2 +8y=20 and y=x+4

To begin you must substitute the value of y provided into the first equation. The would change the equation into the following form:x^2+8(x+4)=20. Now expand the bracket so that the equation becomes:x^2+8x+3...
AM
Answered by Anthony M. • Maths tutor
3549 Views

Differentiate y=x^x with respect to x.

y=x^x, taking natural log of both sides ln(y)=ln(x^x), using laws of logs ln(y)=xln(x), using product rule and implicit differentiation dy/dx 1/y=ln(x)+1 dy/dx=(ln(x)+1)y dy/dx=(ln(x)+1)x^x
Answered by • Maths tutor
4762 Views

Solve the following simultaneous equations. x^2 + 2y = 9, y = x + 3

x^2 + 2y = 9y = x + 3 x^2 + 2y = 9x^2 + 2(x+3) = 9x^2 + 2x + 6 = 9x^2 + 2x - 3 = 0(x + 3)(x - 1) = 0x= -3, x = 1 when x = -3y = x + 3y = (-3) + 3y = 0 when x = 1y = x + 3y = (1) + 3y = 4
JF
Answered by John F. • Maths tutor
3140 Views

Prove that the square of an odd number is always one more than a multiple of 4

If we say n is any number, then we know 2n represents an even number - any number multiplied by 2 is always even. 2n+1 represents an odd number - adding 1 to an even number always gives an odd number (2n + 1...
RR
Answered by Rebecca R. • Maths tutor
3914 Views