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106 results.

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 $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d$ .
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.
Integration: Indefinite integral by substitution
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$
Centroids by integration
Ready to use
Question in Engineering Statics by William Haynes

Find the area, first moment of area, and coordinates of a general spandrel. The area may be above or below the function.
Centroid by integration: upper and lower bounds are functions
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Question in Engineering Statics by William Haynes

Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.
Numbas demo: Motion under gravity
Ready to use
Question in Demos by Christian Lawson-Perfect

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$ . Find time to maximum height and the maximum height. Now includes an interactive plot.
Integrate powers
Draft
Question in DIAGNOSYS by Christian Lawson-Perfect and 3 others

No description given
Differentiate powers
Draft
Question in DIAGNOSYS by Christian Lawson-Perfect and 3 others

No description given
Differential Elements
Ready to use
Question in Engineering Statics by William Haynes

Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration.
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 $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
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 $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$
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 $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$ .
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$ .
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 $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
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 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.
Definite integration 1
Draft
Question in Bill's workspace by Bill Foster

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$ , $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$ , $\int_0^{r}x ^ {2}e^{t x}\;dx$
Definite Integration 2
Draft
Question in Bill's workspace by Bill Foster

Evaluate $\int_0^{\,m}e^{ax}\;dx$ , $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$ .
Integration 4
Draft
Question in Christian's workspace by Christian Lawson-Perfect

Finding areas under graphs using definite integration.
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.
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.

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