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Find the area bounded by the curve y=(sin(x))^2 and the x-axis, between the points x=0 and x=pi/2

First, use the identity cos(2x)=(cos(x))^2-(sin(x))^2 along with the identity (sin(x))^2+(cos(x))^2=1 to obtain the integral of 1/2*(1-cos(2x)) as it is not possible to integrate (sin(x))^2 straight off w...

Answered by Thomas L. • Maths tutor

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Solve the simultaneous equations..... 3x - y + 3 = 11 & 2x^2 + y^2 + 3 = 102 where X and Y are both positive integers.

Here we have two equations with two unknowns, the method we use to solve this is substitution. First, find one of the unknowns in terms of the other by rearranging the first equation to arrive at y = 3x -...

Answered by Reuben W. • Maths tutor

3417 Views

Solve the simultaneous equations y = x^2 - 6x and 2y + x - 6 = 0

Rearrange the second equation in terms of y: meaning that the equation is of the form y = ....-this will give y = 3 - x/2You may now substitute the y in the left hand equation with what y in the right han...

Answered by Tabi D. • Maths tutor

6958 Views

Express (4x)/(x^2-9) - (2)/(x+3) as a single fraction in its simplest form.

First we must expand the demoninator to; (x+3)(x-3)Then we can multiply the left hand fraction on top and bottom by (x-3) to get a common demoninatorthis gives us; (4x)/((x+3)(x-3)) - ((2)(x-3))/((x+3)(x-...

Answered by Eddie E. • Maths tutor

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Solve 4(x-5)=18

There are 2 ways to solve this equation:Method 1:Expand the brackets by multiplying everything inside the brackets by 4 to make 4x-20=18Then +20 to both sides making 4x=38Then divide by 4 to find x, there...

Answered by Jessica S. • Maths tutor

19107 Views