What is Integration?, give me a real life eg.?

Question

What is Integration?, give me a real life eg.
I never understood Integration , Diffreantiation ect, but i kno it is an essintial part of Engineering ( specially Mechanical), so please explain.

Answer 1

Since mechanical engineering often involves the structure, performance, and motion of mechanical objects, integration is often used to provide a detailed theoretical calculation for these characteristics.

If you are a student frustrated and struggling with a mathematical class involving integration, don't worry and do your best. You'll find that engineering applications of math problems tend to make you feel that math is useful after all. That's how I felt. "Duh, I wish someone told me that sooner, now it makes sense." My math grades would have been much better if it didn't feel like calculation for the sake of crunching numbers with no relative meaning.

My favorite course for advanced math were control systems and finite element analysis of structures. I struggled with computational fluid dynamics until I was able to relate it to "unsolvable" math problems!

Answer 2

To calculate the areas of regular figures like triangles, squares, parallelograms and others, you have a formular that has already been derived for you.

However, to calculate the area under an irregular curve like y =x3 or more complex curves, Integration becomes very handy.

Integration is basically the summation of the areas of an infinite number of regular rectangles that can be drawn under the irregular curve, hence the elongated s.

Answer 3

Integration is adding an infinite number of terms together. The integration sign is a modified S.

If you want to find the area/volume of anything integration is the way to go. For example it's the easiest way to prove the area of a circle.

Answer 4

OK, here is a real life example (sorry but it is EE not ME)

Find the DC equivalent of an AC source--> find the rms voltage

Vrms = SQRT[1/T(integral from 0 to T of v(t)^2 dt)]

v(t) = Vpsin(t) Vp = peak voltage

When you get this you find the rms voltage is Vp/SQRT(2)

Answer 5

IntREgration doesnt exist. Integration does. understanding "differential equations" permits you to state ideas mathematically like "the warm temperature flow in a rod is proportional to the adaptation in temperatures of the ends, to the flow sectional section, and the thermal conductivity of the rod". you could make an equation like: dQ=ok*A*dT utilizing non-stop function integration you could remodel this equation into Q=ok*A*(T2-T1) utilizing extremely user-friendly integration. in case you want to habit by the floor of a sphere, or by a rod in a cooling fluid, then you definately want to entice close extra DE and extra Calculus to come back up with an empirically valid equation that describes the actual phenomena. There are 2 subsets of integration: non-stop function integration, and discrete function integration. they provide the effect of being very diverse, and are utilized in diverse elements, besides the undeniable fact that the guidelines of one bring about the formula of the different. in case you want to do mechanical, business, or electric powered engineering then you definately want to stumble on trouble-free methods to love math. study differential equations and calculus. examine by a diff-eq textbook if accessible.

Answer 6

Integration is the inverse of differentiation.
In differentiation, you are given the function and need to calculate its derivative. In integration, you are given a function which is a derivative of something, and you need to recreate the original function.