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Find the area under the curve y = sin(2x) + cos(x) between 0 and pi/2

to find the area integrate the function between 0 and pi/2: indefinite integral of y = -1/2 cos(2x) + sin(x) + c ignore c and input boundary conditions: [-1/2 cos(pi) + sin(pi/2)] - [-1/2 cos(0) + sin(0)] = ...
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Answered by Harry D. • Maths tutor
7959 Views

Given that y = 4x^5 - 5/(x^2) , x=/=0 , find a)dy/dx b)indefinite integral of y

rewrite as y = 4x^5 - 5x^(-2) dy/dx = 20x^4 + 10x^(-3) integral of y = 4x^6 / 6 + 5x^(-1) / 1 + c simplify: 2/3 x^6 + 5/x
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Answered by Harry D. • Maths tutor
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Work out the value of 5^3-5^2:

The first step would be to consider each of the powers individually, work out their value and then proceed with the subtraction to end up with a result. Firstly, as this question is to be done without a calc...
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Answered by Alexander B. • Maths tutor
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Differentiate with respect to x: i) y=x^3ln(2x) ii) y=(x+sin(2x))^3

i) There first step is to acknowledge the need for both product rule (d(uv)/dx=v.du/dx+u.dv/dx) and chain rule (dz/dx=dz/dy*dy/dx). Here, u=x^3 and v=ln(2x). Therefore, du/dx=3x^2 which is a standard differe...
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Answered by Edward M. • Maths tutor
10016 Views

Factorise and solve x^2-8x+15=0

Factorise means we want to turn x 2 -8x+15=0 into the form (x+a)(x+b)=0 . We need to find the two whole numbers 'a' and 'b' which equal -8 (from the -8x part) when added together, i.e. a+b=-8 , and equal 15 ...
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Answered by Anokhi C. • Maths tutor
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