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Application of definite integral in real life?
Finding the area under a curve or the length of a line segment. These are real life uses, not just fun in your math class.
Difference between integral and differential calculus?
Differential calculus is concerned with finding the slope of a curve at different points. Integral calculus is concerned with finding the area under a curve.
How integration is reverse process of differentiation?
For example, the derivate of x2 is 2x; then, an antiderivative of 2x is x2. That is to say, you need to find a function whose derivative is the given function. The antiderivative is also known as the indifinite integral. If you can find an antiderivative for a function, it is fairly easy to find the area under the curve of the original function - i.e., the definite integral.
Discuss line integral and its real life applications?
A line integral can evaluate scalar and vector field functions along a curve/path. When applied on vector field, line integral is considered as measure of the total effect of the vector field along a specific curve whereas in scalar field application, the line integral is interpreted as the area under the field carved out by a particular curve.Line integral has many applications in physics. In mechanics, line integral is used to determine work done by a force in moving an object along a curve. In circuit analysis, it is used for calculating voltage.
Use the concept of a limit to explain how you could find the exact value for the definite integral value for a section of your graph?
The definite integral value for a section of a graph is the area under the graph. To compute the area, one method is to add up the areas of the rectangles that can fit under the graph. By making the rectangles arbitrarily narrow, creating many of them, you can better and better approximate the area under the graph. The limit of this process is the summation of the areas (height times width, which is delta x) as delta x approaches zero. The deriviative of a function is the slope of the function. If you were to know the slope of a function at any point, you could calculate the value of the function at any arbitrary point by adding up the delta y's between two x's, again, as the limit of delta x approaches zero, and by knowing a starting value for x and y. Conversely, if you know the antideriviative of a function, the you know a function for which its deriviative is the first function, the function in question. This is exactly how integration works. You calculate the integral, or antideriviative, of a function. That, in itself, is called an indefinite integral, because you don't know the starting value, which is why there is always a +C term. To make it into a definite integral, you evaluate it at both x endpoints of the region, and subtract the first from the second. In this process, the +C's cancel out. The integral already contains an implicit dx, or delta x as delta x approaches zero, so this becomes the area under the graph.
Geometrically the definite integral gives the area under the curve of the integrand Explain the corresponding interpretation for a line integral?
gemetrically the definite integral gives the area under the curve of the integrand. explain the corresponding interpretation for a line integral.
Definition of integration?
geometically , the definite integral gives the area under the curve of the integrad .
What helps you to find the area under a curve yx34x-3.6?
37.6
What does the area under the curve equal?
The are under the curve on the domain (a,b) is equal to the integral of the function at b minus the integral of the function at a
Application of definite integral in real life?
Finding the area under a curve or the length of a line segment. These are real life uses, not just fun in your math class.
What is integrating?
Integrating is the mathematical process used for finding the area under a curve. In principle, this is accomplished by creating a number of rectangles within the area and summing their areas to get an approximation of the total area under the curve. Obviously, the accuracy of the approximation is related to how closely the rectangles fit to the curve. The more rectangles you have, the closer their summed areas matches the area under the curve. At the point where you have an infinite number of rectangles, their summed area exactly matches the area under the curve. Integration is a mathematical operation performed on the equation of the curve which results in value for the area if the endpoints of the curve are defined (a definite integral) or AA mathematical expression for the area into which endpoints can be plugged (an indefinite integral).
Difference between integral and differential calculus?
Differential calculus is concerned with finding the slope of a curve at different points. Integral calculus is concerned with finding the area under a curve.
How do you draw a momentum -time graph for force-time graph?
The momentum-time graph is the integral of the force-time graph. that is, it is the area under the curve of the f-t graph.The momentum-time graph is the integral of the force-time graph. that is, it is the area under the curve of the f-t graph.The momentum-time graph is the integral of the force-time graph. that is, it is the area under the curve of the f-t graph.The momentum-time graph is the integral of the force-time graph. that is, it is the area under the curve of the f-t graph.
Area under graph?
Is the integral of the curve - between the two end points.
Applications of integral calculus?
Integration can be used to calculate the area under a curve and the volume of solids of revolution.
What is the difference between definite integral and line integral?
Both kinds of integrals are essentially calculations of areas under curves. In a definite integral the surface whose area is to be calculated is planar. In a line integral the surface whose area to be calculated might occupy two or more dimensions. You might be interested in the animated diagrams in the wikipedia article for the line integral.
What is integral in math?
There are two main definitions. One defines the integral of a function as an "antiderivative", that is, the opposite of the derivative of a function. The other definition refers to an integral of a function as being the area under the curve for that function.
