Student calculates $\bar{y}$ for a triangle.  Must use similar triangles get element $dA$.

Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

This easy question is intended to be used by administrators to test the integration of Numbas with a learning environment.

Separable equation for integration.

Integration by parts.

Integration by parts.

Integration by parts.

Integration by parts.

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This easy exam is intended to be used by administrators to check the integration of Numbas with a leaarning environment.

Homework set.  Use integration to find the centroid of shapes bounded by functions.

Homework set.  Use integration to find the centroid of shapes bounded by functions.

 Students must derive the shear and bending moment functions for beam loaded with a parabolic distributed load described with a loading function.  Diagrams are given, but the students must derive the equations by integration.

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 $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution.

Using the various versions of $\cos{2x}$ identity to integrate $\sin^2{x}$ and $\cos^2{x}$.

Calculating the integral of a function of the form $\frac{c}{(x+a)(x+b)}$ using partial fractions.

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

Calculating the integral of a function of the form $a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3}$ using a table of integrals. 

Find roots and the area under a parabola

Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration. 

This easy exam is intended to be used by administrators to check the integration of Numbas with a leaarning environment.

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Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

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

A portfolio of NUMBAS questions created for first year Natural Sciences students. The questions cover the topics: 

• Linear functions
• Quadratic functions
• Differentiation
• Integration
• Explonatial and logarithms 
• Further differentiation
• Further Integration
• Trigonometric Functions

Solving a separable differential equation that describes the rate of decay of radioactive isotopes over time with a known initial condition to calculate the mass of the isotope after a given time and the time taken for the mass to reach $m$ grams. 

Decay Constant - Radioactivity - Nuclear Power (nuclear-power.com)

Calculating area under curves of the form $ax^2+bx$ and $ax^4+bx^3+cx^2+dx+e$ in a contextualised problem.