462 results for "integration".

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• Question

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.

• Centroids by integration
Has some problems
Question

Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

• Question in 1202

No description given

• Question

Find roots and the area under a parabola

• Differential Elements
Question

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.

• Exam (13 questions)

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

• Question in PA1710

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

• Integration by parts
Question in PA1710

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx$ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

• Integration
Question in PA1710

Students must find $\int \frac{1}{x-a} \, dx$.

• Question

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

• Question

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

• Question

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

• Question

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.

• Question

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

• Question

Finding areas under graphs using definite integration.

• Question

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

• Question

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$.

• Question

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

• Question

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.

• Question

Standard simple integrals asked for (1/x, sin(x), cos(x), x^2, x, e^x)

• Question
Multi choice question week 3
• Exam (3 questions)

No description given

• Exam (4 questions)

4 questions on using partial fractions to solve indefinite integrals.

Question

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

Question

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

Question

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

• Question

A sneak peek at a really clever integration of GeoGebra with Numbas.

• Question

Integration by susbtitution, no hint given

• Question

Integration by susbtitution, no hint given

• Question

A function of the form (ax+b)/(x+c) is plotted. Student is asked to calculate the shaded area. Area is both above and below the x-axis.