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Maths
A Level

Use integration by parts to find the value of the indefinite integral (1/x^3)lnx ; integration with respect to dx

Let f denote an integral sign, I will write the integrand in square brackets. The formula for integration by parts is given by:f [(u)(dv/dx)]dx = uv - f [((du/dx)(v)]dxTo apply ...

Answered by Amelia S. Maths tutor
8049 Views

Integrate 2sin^3(x)+3.

First we need to use trigonometric identities to convert the sin^3(x) to a single power. This is because we cannot integrate trigonometric functions that are above the power of 1. We need to use the doubl...

Answered by Vaidik P. Maths tutor
4146 Views

A curve with equation y=f(x) passes through the point (1, 4/3). Given that f'(x) = x^3 + 2*x^0.5 + 8, find f(x).

We know that f'(x) = x^3 + 2*x^0.5 + 8, and we can integrate both sides. This gives us f(x) = (1/4)*x^4 + (4/3)x^(3/2) + 8x + c, remembering to add the constant of integration. Now, we are almost...

Answered by George C. Maths tutor
6075 Views

Find the integral of 4x^2 - 10x + 1/(x^(1/2)), with respect to x, in its simplest form.

= (4/3)x3 - (10/2)x2 + x1/2/(1/2) + C = (4/3)x3 - 5x2 + 2x1/2 + C

Answered by Aisha A. Maths tutor
3191 Views

Can you explain the sum of 1 to 100?

The idea here is to pair your numbers up to get to the solution. If you were to put this through a calculator it would take you a while. However, if we simplify the problem to the sum of 1 to 10 you'll be...

Answered by Jasivan S. Maths tutor
2796 Views

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