522 results for "integration".
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Question in MASH Bath: Question Bank
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)
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Question in MASH Bath: Question Bank
Calculating area under curves of the form $ax^2+bx$ and $ax^4+bx^3+cx^2+dx+e$ in a contextualised problem.
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Question in Skills Audits for Maths and Stats
Calculating the integral of a function of the form $ax^2 \cos(bx)$ using integration by parts.
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Question in Skills Audits for Maths and Stats
Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution.
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Question in Skills Audits for Maths and Stats
Using the various versions of $\cos{2x}$ identity to integrate $\sin^2{x}$ and $\cos^2{x}$.
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Question in Skills Audits for Maths and Stats
Calculating the integral of a function of the form $\frac{c}{(x+a)(x+b)}$ using partial fractions.
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Question in Skills Audits for Maths and Stats
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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Question in Skills Audits for Maths and Stats
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.
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Question in Brendan's workspace
Integration by parts.
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Question in Ugur's workspace
mass of tetrahedron via integration
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Question in How-tos
A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.
If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.
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Question in Engineering Statics
Student calculates $\bar{y}$ for a triangle. Must use similar triangles get element $dA$.
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Question in Engineering Statics
Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.
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Exam (11 questions) in Martin's workspace
Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.
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Exam (17 questions) in Martin's workspace
Quiz designed to test integration of powers of x including negative powers, surds, fractions, etc.
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Question in Brendan's workspace
Separable equation for integration.
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Question in Brendan's workspace
Separable equation for integration.
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Question in Brendan's workspace
Integration by parts.
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Question in Brendan's workspace
Integration by parts.
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Question in Brendan's workspace
Integration by parts.
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Question in Brendan's workspace
Practice question simplifying fractions for integration by using partial fractions.
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Exam (17 questions) in Mobius formative/summative tests
DCS 2023 Maths Entrance Test to be used September 2023
1.5 hours with 3 randomised questions from each of these groups:
- Notation and Algebra
- Calculus - Differentiation
- Calculus - Integration
- Trigonometry
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Question in MASH Bath: Question Bank
Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are given in the question.
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Question in MASH Bath: Question Bank
Calculating the definite integral $\int_{n_1}^{n_2}ax^b dx$.
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Question in Musa's workspace
Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.
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Question in Musa's workspace
Recovering original function given some information such as derivative and value at some point.
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Question in Musa's workspace
Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q} + k/x \;dx$.
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Question in All questions
Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.
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Question in Ugur's workspace
Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.
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Question in MASH Bath: Question Bank
Calculating the integral of a function of the form $4ax(ax^2+b)^n$ using integration by substitution.