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Simple Indefinite Integrals

Real life problems with differentiation

Simple Indefinite Integrals

Real life problems with differentiation

Maximising the volume of a rectangular box

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Chain rule

Quotient rule

Integration by Substitution

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Definite Integrals

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

Basic indefinite integrals, Basic definite integrals, integration by substitution

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Definite Intgerals

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

Antiderivatives

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Finding the stationary points of a cubic with two turning points

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

Introduction to using the product rule

Solve a pair of linear equations by writing an equivalent matrix equation.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.