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CF Maths In class test three question 8 Integration by partial fractions with limits
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Question in Deactivated user's workspace by Jinhua Mathias

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d$ .
Centroid of a triangle by integration
Ready to use
Question in Engineering Statics by William Haynes

Student calculates $\bar{y}$ for a triangle. Must use similar triangles get element $dA$ .
Area of a trapezoid by integration
Ready to use
Question in Engineering Statics by William Haynes

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.
Integration by substitution
Needs to be tested
Question in John's workspace by John Bissell and 1 other

Use a substitution to simplify an integral.
Area under a curve by integration
Ready to use
Question in Engineering Statics by William Haynes

Find roots and the area under a parabola
Integration by partial fractions
Ready to use
Question in Bill's workspace by Bill Foster and 1 other

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.
Numbas demo: video
Ready to use
Question in Demos by Christian Lawson-Perfect

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$ . Solution involves the inverse trigonometric function $\arcsin$ .
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$ . Solution involves inverse trigonometric functions.
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
Leicester: Integration 3
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx$ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx$

Also two other questions on integrating by parts.
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$ .
Hyperbolic Functions 4
Draft
Question in Bill's workspace by Bill Foster

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$
Hyperbolic Functions 3
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$
Volume of revolution 2
Draft
Question in Bill's workspace by Bill Foster

Rotate the graph of $y=a\ln(bx)$ by $2\pi$ radians about the $y$ -axis between $y=c$ and $y=d$ . Find the volume of revolution.
Volume of revolution 1
Draft
Question in Bill's workspace by Bill Foster

Rotate $y=a(\cos(x)+b)$ by $2\pi$ radians about the $x$ -axis between $x=c\pi$ and $x=(c+2)\pi$ . Find the volume of revolution.
Integration by substitution
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.
Use Green's theorem to convert line integral to double integral,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$ .
Calculate line integral over a straight line
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Find $\displaystyle \int_{\Gamma} \left(x+y \right)\;dx+\left(y-x\right)\;dy,\;\Gamma$ is the line from $(0,0)$ to $(a,b)$ .
Evaluate double integrals with numerical limits,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Double integrals (2) with numerical limits
Compute Riemann sums on an interval
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximating integral of a quadratic by Riemann sums . Will include an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.
Compute Riemann sums of a quadratic function
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.
Compute Riemann sums of a linear function,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.
Compute Riemann sums of a linear function,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.
Approximate the integral of a quadratic by Riemann sums,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.
Integral by hyperbolic substitution
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$
Definite integration using standard integrals
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Calculate definite integrals: $\int_0^\infty\;e^{-ax}\,dx$ , $\int_1^2\;\frac{1}{x^{b}}\,dx$ , $\; \int_0^{\pi}\;\cos\left(\frac{x}{2n}\right)\,dx$

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