Pls explain the concept of differentiation and integration. It's urgent!!
Answers
Answer:In simple terms, differentiation is the act of finding the rate of change of the gradient/slope of any function while integration is the area under the curve of function with respect to the x axis.
Explanation:
Answer:
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Explanation:
Differentiation is the essence of Calculus. A derivative is defined as the instantaneous rate of change in function based on one of its variables. It is similar to finding the slope of a tangent to the function at a point.
Suppose you need to find the slope of the tangent line to a graph at point P. The slope can be approximated by drawing a line through point P and finding the slope by a line that is known as the secant line.
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A function f in x is said to be differentiable at the point x = a if the derivative f'(a) exists at every point in its domain. The differentiation formula is given by:
differentiation and integration 1
For a function to be differentiable at any point x=a in its domain, it must be continuous at that particular point but vice-versa is necessarily not always true. The domain of f’(x) is defined by the existence of its limits.
If y = f(x) is a function in x, then the derivative of f(x) is given as dy/dx . This is known as the derivative of y with respect to x.
Also, the derivative of a function f in x at x = a is given as:
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The derivative of a function f(x) signifies the rate of change of the function f(x) with respect to x at a point a lying in its domain.
If the derivative of the function, f’, is known which is differentiable in its domain then we can find the function f. In integral calculus, we call f as the anti-derivative or primitive of the function f’. The method of calculating the anti-derivative is known as anti-differentiation or integration