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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
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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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Oxygen is exchanged between the blood capillaries and the tissues. Give two ways in which capillaries are adapted for exchanging blood with the tissues.

Thin walls for short diffusion path 2. Narrow, so have a large surface area to volume ratio
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Answered by Leila G. • Biology 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
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