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Integration formulae
The 11 results the integration notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 11, the formulae booklet prints 1, 7 are yours to memorise and 3 are working lines the notes derive in front of you.
Years 12-13 · 6 lessons with formulae.
A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.
∫ xn dx = xn+1n + 1 + c (n ≠ −1)∫ x^n dx = x^(n + 1)/(n + 1) + c (n ≠ − 1) NOT IN THE BOOKLET: LEARN ITConditionsn ≠ −1, as the formula states, and an interval that avoids x = 0 when n is negative. ∫ cos kx dx = 1ksin kx + c∫ cos kx dx = (1/k) sin kx + c NOT IN THE BOOKLET: LEARN ITConditionsk ≠ 0, x in radians. ∫ sin kx dx = −1kcos kx + c∫ sin kx dx = −(1/k) cos kx + c NOT IN THE BOOKLET: LEARN ITConditionsk ≠ 0, x in radians. ∫ ekx dx = 1kekx + c∫ e^kx dx = (1/k)e^kx + c NOT IN THE BOOKLET: LEARN ITConditionsk ≠ 0. ∫ 1x dx = ln|x| + c∫ (1/x) dx = ln|x| + c NOT IN THE BOOKLET: LEARN ITConditionsx ≠ 0, and the constant may differ on each side of zero. ∫ f'(x)f(x) dx = ln|f(x)| + c∫ (f′(x)/f(x)) dx = ln|f(x)| + c NOT IN THE BOOKLET: LEARN ITConditionsf(x) ≠ 0 right across the interval of integration. ∫ u dvdx dx = uv − ∫ v dudx dx∫ u (dv/dx) dx = uv − ∫ v (du/dx) dx IN THE FORMULAE BOOKLETConditionsu and v differentiable on the interval. ∫ 23x + 5 dx = 23ln|3x + 5| + c∫ (2/(3x + 5)) dx = (2/3) ln|3x + 5| + c NOT IN THE BOOKLET: DERIVED IN THE LESSONConditionsThe interval of integration must not contain x = −5/3. area = ∫ y dxdt dtarea = ∫ y (dx/dt) dt NOT IN THE BOOKLET: LEARN ITConditionsx and y differentiable in t, limits taken as the t values at the ends, and y ≥ 0 for the integral to measure the area. limδx → 0 Σ f(x) δx = ∫ab f(x) dxlim_(δx → 0) Σ f(x) δx = ∫_a^b f(x) dx NOT IN THE BOOKLET: DERIVED IN THE LESSONConditionsf integrable on [a, b], with the strips covering the interval and their width tending to zero. ∫ 1g(y) dy = ∫ f(x) dx∫ (1/g(y)) dy = ∫ f(x) dx NOT IN THE BOOKLET: DERIVED IN THE LESSONConditionsThe equation must separate as dy/dx = f(x)g(y), and g(y) ≠ 0. Values with g(y) = 0 are constant solutions that dividing throws away. Every formula in the library is indexed by unit on the equation index, and the integration notes are where these results are derived and used. The 7 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.
Also: Differentiation formulae · Numerical methods formulae