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Sketch the graph of x^2+y^2-6x-4y=23

Firstly, to try and sketch this graph just going on the equation as it is above is a huge task for any maths student. The best way to approach this is to neaten it up with some algebra: -1: x^2+y^2-6x-4y can...
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Answered by Sam A. • Maths tutor
8745 Views

Integrate the function f(x) = ax^2 + bx + c over the interval [0,1], where a, b and c are constants.

Firstly remember that d/dx(x^n) = nx^(n-1). And so the antiderivative, or integral of x^n, i.e. \int(x^n) = x^(n+1)/(n+1) + C (where C is the integration constant). When integrating with limits, i.e. when we...
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Answered by Anvarbek A. • Maths tutor
5489 Views

Find the general solution, in degrees, of the equation 2sin(3x+45°)=1. Use your general solution to find the solution of 2sin(3x+45°)=1 that is closest to 200 °.

The first thing to do when we are facing a trigonometry problem is to to draw the sine and cosine diagram on the unit circle. That takes very little time to do and is incredibly helpful to visualize the peri...
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Answered by Francesco S. • Maths tutor
6598 Views

Find the area under the curve y = (4x^3) + (9x^2) - 2x + 7 between x=0 and x=2

To be able to solve this, the equation needs to be integrated. To do this, simple integration needs to be applied where the power of 'x' increases by 1 and the coefficient of 'x' is divided by the new power....
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Answered by Yash S. • Maths tutor
5400 Views

Find INT{2,1}{x^4 + 3x^2 + 2}

This is a typical AS-level Maths question. We see it’s a definite integral so start by drawing some big square brackets with the “limits” (2 and 1). We go through the expression inside the integral (the “int...
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Answered by Andrew F. • Maths tutor
4235 Views