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

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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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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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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

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Indefinite Integrals

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Simple Indefinite Integrals

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

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Three forces act on a particle. You're given the magnitude of one, and the directions of all three. Find the magnitudes of the other two forces.

A particle is in equilibrium on an incline. Four forces are acting on it. You're given the angle of the incline and three forces. Resolve the forces to find the angle and magnitude of the other force.

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A ball is thrown vertically upwards from a position above ground level. Find its greatest height, and the total time its in the air.

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Basic indefinite integrals, Basic definite integrals, integration by substitution

Missing: Area type question, solving diff eq application

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Calculations involving elementary probability, and several questions designed to draw out misconceptions to do with probability.

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

A function which renders the factorisation of a number in LaTeX.

Calculate the midpoint of two points.

Identifying y=mx+b given two points