Algebra Pre-Algebra and Basic Algebra Math Forum

April 22nd, 2018, 12:45 AM   #1
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Integral

What is the integral of the mathematical expression in the picture:
Attached Images integral.png (1.3 KB, 18 views) April 22nd, 2018, 12:53 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra That's an inequality. You can't integrate an inequality. However, we can integrate the left hand expression of the inequality by a substitution of $u=x+1$. Alternatively, \begin{align*}\frac{x^2}{x+1} &= \frac{(x+1)^2 - 2x - 1}{x+1} \\ &= \frac{(x+1)^2 - 2(x+1) + 1}{x+1} \\ &= (x+1) - 2 + \frac1{x+1} \\ &= x - 1 +\frac1{x+1}\end{align*} Last edited by v8archie; April 22nd, 2018 at 01:02 AM. April 22nd, 2018, 12:58 AM   #3
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Quote:
 Originally Posted by shaharhada What is the integral of . . .
Did you mean “integral”? You posted in Algebra, not Calculus. April 22nd, 2018, 01:05 AM   #4
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This is my solution.
Is it wrong?
Attached Images integral solution.png (2.3 KB, 0 views) April 22nd, 2018, 01:13 AM #5 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 The fact that f(x)< 1 does NOT mean that $\displaystyle \int f(x)dx< 1$! For one thing, a indefinite integral like this always includes an arbitrary constant. The integral can be larger or less than 1 depending upon that constant. For a definite integral it is true that if $\displaystyle f(x)< 1$ then $\displaystyle \int_a^b f(x)dx< b- a$. Thanks from topsquark April 22nd, 2018, 01:40 AM   #6
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And if the f(x) < 2, is it the same?
Can you give some examples for:
Quote:
 Originally Posted by Country Boy;593137 For a [b definite[/b] integral it is true that if $\displaystyle f(x)< 1$ then $\displaystyle \int_a^b f(x)dx< b- a$. Tags integral Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Jhenrique Calculus 5 June 30th, 2015 04:45 PM gen_shao Calculus 2 July 31st, 2013 10:54 PM maximus101 Calculus 0 March 4th, 2011 02:31 AM xsw001 Real Analysis 1 October 29th, 2010 08:27 PM maximus101 Algebra 0 December 31st, 1969 04:00 PM

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