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Integration
We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative (rate of change) of a function F(x) and is denoted by F'(x) Often, we may know the rate of change, F'(x) of a function F(x) which is unknown to us. In such situations we would like to find out the original function F(x) from the derivative, F'(x). Reversing the process of differentiation and finding out the original function from the derivative is called integration. The original function, F(x) is called the integral.
The left hand side of the equation is read as "the indefinite integral of f(x) with respect to x. The symbol is the integral sign, f(x) is the integrand and 'c' is an arbitrary constant. The arbitrary constant 'c' is added because of the following reason:
If d/dx {F(x)} = f(x) then we can also write that d/dx {F(x) + c} = f(x) where 'c' is an arbitrary constant, because the derivative of any constant is zero.
A pair of mittens has been discounted 12.5%. The original price of the mittens was $10. What is the new price? Find 12.5% of $10 and subtract it from $10. Find out 12.5% of $10
So far we have considered differentiation of functions of one independent variable. In many situations, we come across functions with more than one independent variable
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Paulina played 3 soccer games on Saturday she drank I juice box during each soccer game how many juice boxes did she drank
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Evaluate following limits. Solution Let's begin with the right-hand limit. For this limit we have, x > 4 ⇒ 4 - x 3 = 0 also, 4 - x → 0 as x → 4
Callie's grandmother pledged $0.50 for each mile Callie walked in her walk-a-thon. Callie walked 9 miles. How much does her grandmother owe? Multiply the number of miles (9) th
1. Solve the given differential equation, subject to the initial conditions: . x2y''-3xy'+4y = 0 . y(1) = 5, y'(1) = 3 2. Find two linearly independent power series soluti
How do you find the area of a circle given the diameter?
Prove: 1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA
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