Definite Integral

This calculus video tutorial provides a basic introduction into the definite integral. It explains how to evaluate the definite integral of linear functions, rational functions, and those involving natural log functions. The indefinite integral gives you the antiderivative function in terms of x where as the definite integral gives you a specific number or constant as an answer. This video explains how to evaluate definite integrals using the fundamental theorem of calculus part 2. This tutorial contains plenty of examples and practice problems.
Antiderivatives:
• Antiderivatives
Basic Integration Problems:
• Basic Integration Prob...
Indefinite Integral:
• Indefinite Integral
Definite Integral:
• Definite Integral
Differential Equations:
• Finding Particular Sol...
_______________________________
Properties of Definite Integrals:
• Properties of Definite...
Rectilinear Motion Problems:
• Rectilinear Motion Pro...
Sigma Notation - Calculus:
• Summation Formulas and...
Riemann Sums - Area:
• Riemann Sums - Left En...
The Midpoint Rule:
• Midpoint Rule & Rieman...
________________________________
Finding Area - Limit Definition:
• Finding The Area Using...
Definite Integrals - Geometry:
• Evaluating Definite In...
Fundamental Theorem - Part 1:
• Fundamental Theorem of...
Fundamental Theorem - Part 2:
• Fundamental Theorem of...
Net Change Theorem:
• Net Change Theorem - C...
__________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/mmWmlYClqsiJnNU

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Thank you so much man, never understand definite integrals until now (the night before the exam) because my teacher teaches us like we already learned this before so when he gives his lectures it doesn't make any sense to me. Thank you

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[@Diaryofaninja]

For the problem presented at 6:15 this is wrong. You can only evaluate the integral like that if the function is continuous from a to b which it isn’t, there’s a V.A at x=0. You have to separate it.

[@serbanhoban1517]

Exactly, and if you separate it you will find that the integral diverges

[@_buany8701]

This because I just watched a video where he said you couldn’t do this so now I’m confused

[@andredubbs4854]

@@_buany8701 just watch the graph of the function on a desmos. try to find the area from -3 to 4, you'll see a vertical asymptote at x = 0. Which means your definite integral is infinite, you have an infinite area kinda, its a big ass space lmao.

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I can't understand definite integration through my maths teacher despite him explaining that in our native language and this guy speaks in English I am able to understand this way more better.

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4:00-4:35: the constant isn't needed in definite integrals because it cancels out. That's what I needed to know! Thank you.

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For the problem at 7:30, wouldnt you have to take the lim as a approaches 0 from the left, and the lim as b approaches 0 from the right, since the denominator of the oroginal function is x?

[@JKMath]

He definitely should have taken into consideration that the function is not defined at x=0. This normally would not be a problem if the bounds did not include 0. For example, if the bounds were 1 and 4 rather than -3 and 4, then his approach to solving that integral would be correct since 0 is not included between those bounds, just 1, 2, 3, and 4 would be. However, since the bounds are -3 and 4, the value of 0 is included between them, and so you would be correct in saying that a different method of solving would be necessary. So for anyone taking a calc 1 course, don't worry about coming across this type of problem until you take a calculus 2 course, or cover the concept of improper integrals. Hope this helps!

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The way my professor solve definite integral is so different, he use the power rule first before proceeding to the deffinite formula which brought me alot of confusion.

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Professor Organic Chemistry Tutor, thank you for explaining the differences between the Definite and the Indefinite Integral in Calculus. This topic is used every day in Advanced Mathematics. Professor Organic Chemistry Tutor, at the 6:15 minute mark, the integral of 8 divided by x cubed from minus three to four is infinite. This is an improper integral in Calculus. In the final example, there is an absolute value sign missing after the ln. Please correct these errors in the video.

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6:05 This one was done incorrectly. 8/x^3 is not integrable on the interval (-3, 4).

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WIth the problem at 8:47, would it be fine to integrate the integrand the same way as the previous question so that x^-1 becomes x^0/0? Which in turn becomes 5(1) = 5? Nvm dividing by zero prolly not a good idea l0lz

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