412 results for "integral".
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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
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
Double integral in polar coordinates - concentric circles
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Exam (9 questions) in Ugur's workspace
set of exercises on double and triple integrals
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Question in Brendan's workspace
First order integral.
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Question in Brendan's workspace
First order integral.
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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 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
Definite Intgerals
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Question in Musa's workspace
Definite Integrals
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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 Question authoring examples
This question is the one described in method 2 of the example "Apply a standard integral" in the Numbas documentation.
The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.
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Question in Ugur's workspace
Volume of a tetrahedron using integrals
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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 Ugur's workspace
Inputing Integrals tutorial
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Question in Ugur's workspace
3 Repeated integrals of the form $\int_a^b\;\int_c^{f(x)}g(x,y)\;dy \;dx$ where $g(x,y)$ is a polynomial in $x,\;y$ and $f(x)$ is a degree 0, 1 or 2 polynomial in $x$.
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Question in Ugur's workspace
Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;\int_0^{x^{m-1}}mf(x^m+a)dy \;dx$
The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.
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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.
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Question in MASH Bath: Question Bank
Integrating a function of the form $\frac{a}{x}$ using a table of integrals / anti-derivatives.
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Question in John's workspace
Use a substitution to simplify an integral.
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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 not given in the question and must be calculated.