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Why does integration by parts work?

Let's consider the form of the formula we use for integration by parts: the integral of u * dv/dx = uv - the integral of v * du/dx. We know that integration is the inverse of differentiation, so we should...

Answered by Tomas S. • Maths tutor

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Find the area enclosed by the curve y = cos(x) * e^x and the x-axis on the interval (-pi/2, pi/2)

To find the area enclosed by a function, we need to use integration. Here, the function is not easy to integrate just by inspection, but it is the product of two functions we do know how to integrate: cos...

Answered by Tomas S. • Maths tutor

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What is differentiation and how do I do it?

explain the following briefly: To work out the gradient, first principles, shortcutsexplain in detail: different methods

Answered by • Maths tutor

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Given that: y = 3x^2 + 6x^1/3 + (2x^3 - 7)/(3x^1/2), x > 0 Find dy/dx, give each term in its simplest form

y = 3x² + 6x^1/3 + (2x³/3 - 7/3)x^-1/2Using the multiplication rule for indices y = 3x² + 6x^1/3 + (2/3)x^5/2 - (7/3)x^-1/2

Answered by • Maths tutor

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Solve the simultaneous equations x+2y=4 and x-3y=6

This can be solved in two ways, by substitution or by elimination.Firstly, by substitution, rearrange the first of the two equations in terms of x by subtracting 2y from both sides to get x=4-2y. Then plu...

Answered by Hamish M. • Maths tutor

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