Simple Indefinite Integrals

Simple Indefinite Integrals

Simple Indefinite Integrals

Simple Indefinite Integrals

Simple Indefinite Integrals

Simple Indefinite Integrals

Simple Indefinite Integrals

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.

Simple Indefinite Integrals

Algebra word problems using area and perimeter.

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Calculating wages using algebraic equations

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A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

Differentiation question with customised feedback to catch some common errors and corresponding partial marks.

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Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Shows how to define variables to stop degenerate examples.

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Rearranging equations to change the subject

Another transposition question, which requires (basic) factorisation.

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rearranging the Michelas-Menten equation to make the substrate the subject.

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Partial differentiation question with customised feedback to catch some common errors.

Simple ratio question with custom marking and partial credit possible

The marking checks for some common errors and awards partial credit and appropriate feedback. The errors that give different levels of partial credit include: forgetting to add one to the denominator, forgetting to change to a percentage.

Indefinite Integrals

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Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

5 questions on using substitution to find indefinite integrals.

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

4 questions on integrating by parts.