A variety of trigonometric equations which can be solved using inverse operations.

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Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution, no hint given

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Integration by susbtitution, no hint given

Integration by susbtitution, no hint given

Integration by susbtitution, no hint given

Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution, no hint given

Integration by Substitution

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rebel

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 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.

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.

4 questions on integrating by parts.

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.

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

rebelmaths

Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$. Enter the constant of integration as $C$.

5 indefinite integrals containing exponential functions

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Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

Rate of change problem involving velocity & acceleration

Rate of change problem involving velocity & acceleration

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Integration by susbtitution, no hint given

Step by step solving for integration by substitution

Basic indefinite integrals, Basic definite integrals, integration by substitution

Missing: Area type question, solving diff eq application