Questions which rely on knowledge of standard integrals.

Find the integral of an improper fraction.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

4 questions on integrating by parts.

5 questions on using substitution to find indefinite integrals.

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

Integration by Substitution

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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

Basic indefinite integrals, Basic definite integrals, integration by substitution

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5 questions on indefinite integration. Includes integration by parts and integration by substitution.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

5 questions on using substitution to find indefinite integrals.

4 questions on integrating by parts.

4 questions on using partial fractions to solve indefinite integrals.

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

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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Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Two masses in a box which is attached to a string. Finding acceleration by modelling the two masses as the whole system. Find forces exerted by the two masses.

Finding the acceleration of a particle on an inclined plane which is at an angle to the horizontal. Smooth then with value for coefficient of friction.

A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.

A caravan pulled along by a car. Question uses SUVAT equations and $F=ma$.

Find roots and the area under a parabola

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

Find $\displaystyle \int (ax)\ln(cx)\; dx $

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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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.

Find roots and the area under a curve

Basic indefinite integrals, Basic definite integrals, integration by substitution

Missing: Area type question, solving diff eq application