Anybody want to solve this??ÿ
(It's been fifty years or more since I worked with integrals)
Simply reading that word makes my head hurt and instills nightmares of long ago and far away.
I had a calculus instructor years ago that acted and looked like our friend Kent.?ÿ My hardheadedness pushed him to his limits of restraint.?ÿ I made it out of there with a low C.?ÿ When the semester was over he confided in me that he was glad I was gone.?ÿ I told him we both finally agreed on something.
Long time for me, too. Not sure I will be able.
Pedantic point: one may "evaluate the expression", but it is not an equation so it can't be "solved."
@dougie I know the F(U) part but my integrals only grow in my butt...
That was the same feeling with my Series and Differential Equations (fourth semester of calculus) teacher.?ÿ I believe he raised my final score on the semester exam to make sure I would not be returning under any conditions.?ÿ I sang.?ÿ I danced.?ÿ I made like a fool.?ÿ Free at last!?ÿ Free at last!
About a year and a half later I was taking an electrical engineering class and the instructor taught me everything I did not understand while sliding through the four semesters of calculus.?ÿ Life would have been much simpler if he had been the calculus instructor.?ÿ Somehow his communications and my receptions meshed.?ÿ Things that had been blurry became clear.?ÿ Nice guy.?ÿ Refused to let us call him anything but his first name instead of instructor or professor or doctor.?ÿ He was a farmer's kid that had the gray matter to do most anything he put his mind to do.?ÿ Made a point to return to the farm every time he had a chance as he loved it.
Thanks, Wayne.
We can graph the function that's being integrated and at least determine the sign of the answer. The Foo Plot online grapher gives this:
The integral is the area from the y-axis to x = 1 between the curve and the x-axis. Since the curve is below the x-axis, the area is negative. Just eyeballing the graph as a rectangle, the answer should be somewhere around -3, maybe give or take a fair amount.?ÿ
?ÿ
All I think I know about it is the limits are from 0 to 1. I think. ?????ÿ
OK Dave what's this for ?
?ÿanswer:?ÿ?ÿ?ÿ?ÿ?ÿ(17/12) +4 Ln[3-2*sqrt2]?ÿ?ÿ Note: Ln is the natural log; or Log to the base e
or?ÿ -5.634322 +
JOHN NOLTON
PS?ÿ Wait for a check from MathTeacher
I know this one!
42!
?ÿ -5.634322 +
If the graph above is correct, the answer cannot be more negative than -3.5, as the area is contained within a 1x3.5 rectangle
@bill93 I did not see mathteacher post when I posted. See my note to Dave to wait till MathTeacher checks my work.
See also my post below.
Dave my corrected answer is?ÿ 1/16(-202 sqrt2 ?ÿminus 135 *Ln(3-2*sqrt2) = -2.98127
?ÿ
JOHN NOLTON
simple little things get me every time!
Dave I like your answer but 42 would be for Integral from zero to 3 of x^2 * sqrt (x^3+9) dx
When I did Lindell's problem (and thanks to mathteacher after seeing his graph I went back and found MY error
I saw the number 42 in a Calculus book of mine).
See Calculus with Analytic Geometry by Edwards & Penney, 4th edition page 309
When I started college, I was headed toward the dark side and signed up for Calculus.
What I got from Calculus is that there are no wrong answers when you can design a problem to fit what you have.
Every other statement, no, every statement the Professor said began "What if".
If the Professor can't decide or know what, then he's not going to teach me "what is" and he didn't.
Differential Equations, Trig and Linear Algebra were my game thru the 70s.
A few summers ago, I got lost trying to show a group of techs how I would solve acreage problems using triangles.
Carlson has been telling me what things are since 1983.
0.02
Yeah, me too, except that I use different software. John Nolton's second answer, ~ -2.98, is correct, but I used a computer algebra system to compute the numeric answer without doing the indefinite integral.
The steps for doing the indefinite integral and evaluating the answer are here: https://www.symbolab.com/solver/step-by-step/%5Cint_%7B0%7D%5E%7B1%7D%5Cfrac%7B3x%5E%7B3%7D-x%5E%7B2%7D+2x-4%7D%7B%5Csqrt%7Bx%5E%7B2%7D-3x+2%7D%7Ddx
Pretty involved, huh?
"My hardheadedness pushed him to his limits of restraint."
Word of caution": Don't try this with a Nun. I have and it ain't pretty. ????
I had a Calculus teacher (Calc III?) who wrote on the blackboard (yeah we still used them then) with his right hand and erased with his left.?ÿ If you were listening to what he said you didn't have time to copy what he wrote.?ÿ If you copied what he wrote you couldn't pay attention to what he was saying.?ÿ I lasted about two weeks before dropping that course.
Andy