Simple Indefinite Integrals

Basic indefinite integrals, Basic definite integrals, integration by substitution

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Simple Indefinite Integrals

Simple Indefinite Integrals

Simple Indefinite Integrals

Basic indefinite integrals, Basic definite integrals, integration by substitution

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Definite Integrals

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

Basic indefinite integrals, Basic definite integrals, integration by substitution

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Definite Intgerals

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Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

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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Indefinite Integrals

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Definite Integrals

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5 indefinite integrals containing exponential functions

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Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

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

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$

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

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

Definite Integrals

Definite Intgerals

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Definite Integrals

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Trigonometric Integral

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Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

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

Improvements needed:

• Add some definite integrals to Q2
• Use different variables

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.