Solving using Tables of integrals

calcisfun

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Hi, I am stuck on a homework problem, we are supposed to be using the tables of integrals to figure it out and I am blanking on it. It can be done as integrating by parts, but for the purpose of concept we are to use the tables of integrals. If someone can help me out I would appreciate it, I have done it by parts, and can get to the answer, but cannot find a form on the tables of integrals that work.
calcproblem.png
 
Hi, I am stuck on a homework problem, we are supposed to be using the tables of integrals to figure it out and I am blanking on it. It can be done as integrating by parts, but for the purpose of concept we are to use the tables of integrals. If someone can help me out I would appreciate it, I have done it by parts, and can get to the answer, but cannot find a form on the tables of integrals that work.
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If I were to do this problem - I would have first substituted:

x = (3/5) * sin2(u)

Upon simplification, that should produce a recognizable function and you can use the tables for integrals.
 
A lot depends on what your particular integral table contains!

I just pulled out the book of tables I got in college, whose integral table has almost 600 integral forms. One of them is #128, under the heading, "Forms containing [MATH]\sqrt{a+bx}[/MATH]": [MATH]\int \frac{\sqrt{a+bx}}{x}dx[/MATH]. If your table includes that, use it. If not, what does it include that is relevant?
 
Hi, I am stuck on a homework problem, we are supposed to be using the tables of integrals to figure it out and I am blanking on it. It can be done as integrating by parts, but for the purpose of concept we are to use the tables of integrals. If someone can help me out I would appreciate it, I have done it by parts, and can get to the answer, but cannot find a form on the tables of integrals that work.
View attachment 14294
To me the integrand is clearly in the form sqrt(a-x)/x. The reason I did not say sqrt(a-bx)/x is because you can factor out the b. If this is NOT in your table then to answer your question we need to see you list of integrals on that table.
 
Flabbergasted is not to strong a description to describe my reaction to this post.
Look at this. Anyone who has a smart phone can walk around with WolframAplpha in pocket.
Integral tables? Give me a break is this the 1970's?
I am sure I have posted this before. As a young Assistant Prof. in a new position, I was assigned a service course for mathematics-education majors: probability&stat. About four weeks into the course the instructor who always had taught the course paid me a visit. Man was he hot, students had been to see him about my teaching. He explained that for years he spent the first five weeks teaching how to find the square roots of various numbers. When I showed him a calculator(which by today's standards was no more than a slide rule) he went the Dean to tell him was going to ruin the students with new ideas.
 
In some parts of the world, logarithm tables are still an important part of the curriculum, and calculators are banned for important exams. In order to help students, we unfortunately sometimes have to help them work within archaic systems.

But even modern textbooks typically have a short integral table; and looking up an integral is far more reasonable than making them do all the work all the time (particularly given that smart phones are not typically allowed on exams). Some sort of balance is needed.

I'm interested to see what sort of table is provided in this case. That will make all the difference.
 
Hi, I am stuck on a homework problem, we are supposed to be using the tables of integrals to figure it out and I am blanking on it. It can be done as integrating by parts, but for the purpose of concept we are to use the tables of integrals. If someone can help me out I would appreciate it, I have done it by parts, and can get to the answer, but cannot find a form on the tables of integrals that work.
View attachment 14294
Substitute (the instruction did not forbid use of other methods in conjunction with "tables"):

x = (3/5)*sin2(u)

dx = (6/5)*sin(u)*cos(u) du

35x dx =3cos(u)65sin(u)cos(u)du\displaystyle \sqrt{3-5x} \ dx \ =\sqrt{3} * cos(u) * \frac{6}{5} * sin(u) * cos(u) du

35x2x dx =3cot(u)cos(u)du\displaystyle \frac{\sqrt{3-5x}}{2x} \ dx \ = \sqrt{3} * cot(u) * cos(u) du

Now look-up your integration table.

Substitute back for 'u'.

Finally, check your answer with WA to make pka happy!;);)
 
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