The first set represents how to get the graph of the derivative v from the graph of the function x by taking the slope "little triangles" or "rise over run". These equations show what is going on:. We start with the x-t graph. At each time on the x-t graph 5 are shown by dotted lines we make small triangles showing what the change is in x during a small time interval around each selected instant.
The ratio of those two changes is the velocity at that instant. To go backwards — from velocity to position — we have to integrate. That process is represented by these graphs. The derivative is the ratio so So you should really know about Derivatives before reading more! After the Integral Symbol we put the function we want to find the integral of called the Integrand ,.
It is the "Constant of Integration". It is there because of all the functions whose derivative is 2x :. So when we reverse the operation to find the integral we only know 2x , but there could have been a constant of any value. Is there any practical use of integration? What is the most important prerequisite for Stochastic calculus?
Can you enlighten me with regards to above set of questions please? Community Bot 1. Is there any prectical use of addition? All physics is based on integrals. How to compute the average of a function on a given interval? How to compute the trajectory of a mobile from speed and initial location?
What is the chemical potential? Plus, the integral symbol is one of the most beautiful symbols in math IMO! In fact until I saw that link in my question, I thought integration was important although I didn't know why.
Now that claude and zeta pointed out, I will read further to have a better understanding. It is just that I also saw finding anti derivative of certain functions take lots of undetermined coefficients There were lots of prctical scenarios discussed.
However in terms of intergrals I am yet to dive in. I should have reserached more reckon Show 1 more comment. Active Oldest Votes. Calculus and probability theory not statistics! Exponential and Logarithmic functions 7. Derivatives of the exponential and logarithmic functions 8. Implicit Differentiation 9. Inverse Trigonometric Functions Limits revisited Hyperbolic Functions 5 Curve Sketching 1.
Maxima and Minima 2. The first derivative test 3. The second derivative test 4. Concavity and inflection points 5. Optimization 2.
Related Rates 3. Newton's Method 4. Linear Approximations 5. The Mean Value Theorem 7 Integration 1. Two examples 2. The Fundamental Theorem of Calculus 3. Some Properties of Integrals 8 Techniques of Integration 1. Substitution 2. Powers of sine and cosine 3. Trigonometric Substitutions 4. Integration by Parts 5.
Rational Functions 6. Numerical Integration 7. Additional exercises 9 Applications of Integration 1. Area between curves 2. Distance, Velocity, Acceleration 3.
Volume 4.
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