Calculating the integral of a function of the form $\ln(ax)$ using integration by parts.

Calculating the integral of a function of the form $ax^2 e^{bx}$ using integration by parts.

Calculating the integral of a function of the form $ax^2 \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $x^n \ln(ax)$ using integration by parts.

Calculating the integral of a function of the form $(a+bx)\cos(x)$ using integration by parts.

Calculating the integral of a function of the form $ax e^{bx}$ using integration by parts.

Calculating the integral of a function of the form $ax \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $ax \sin(bx)$ using integration by parts.

Calculating the area enclosed between a cosine function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Calculating the definite integral $\int_{n_1}^{n_2}a \sin(bx) dx$, where $n_1$ and $n_2$ are multiples of $\frac{\pi}{12}$.

Calculating the definite integral $\int_{n_1}^{n_2}a \sin(bx) dx$, where $n_1$ and $n_2$ are multiples of $\frac{\pi}{12}$.

Calculating the definite integral $\int_{n_1}^{n_2}a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3} dx$.

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Indefinite integration of basic functions.

No time limit - unlimited regeneration of questions allowed from these groups:

• Notation and Algebra
• Calculus - Differentiation
• Calculus - Integration
• Trigonometry and Matrices

Definite integation of basic functions.

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

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

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

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

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

Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.  

A simple question to find the roots of a quadratic. Using to test integration of NUmbas into Canvas.

Integrate the product of two functions by the method of integration by parts.

This is a formative assessment and your score is not recorded. This tests assess integration by substitution. You should be able to use the appropriate substution and then use the integral table.

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