Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

Basic indefinite integrals, Basic definite integrals, integration by substitution

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Integration by Parts

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5 indefinite integrals containing exponential functions

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Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Integration by Substitution

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Integration by susbtitution, no hint given

Integration using partial fractions

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Integration by parts

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This quiz is designed to help you practise your integration techniques.

Improvements needed:

• Add some definite integrals to Q2
• Use different variables

This quiz is designed to help you practise your integration techniques.

Find $\displaystyle I=\int \frac{2 a x +b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Finding areas under graphs using definite integration.

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Integration by Substitution

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Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

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Finding areas under graphs using definite integration.

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Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

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indefinite integration

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

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Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Integration by parts, trigonometric integrals, partial fractions, complete the square

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Integration by Substitution

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Practice partial fractions. Preparing for integration using partial fractions.

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Find an integral by choosing a suitable substitution.

A sneak peek at a really clever integration of GeoGebra with Numbas.

Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.