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Integration Calculator

# Integration Calculator

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Integration is a very important concept in mathematical calculus. Integration means finding the anti-derivative of the given function. Therefore integration of a function f(x) is ‘F(x)’ where f(x) is the derivative of the function F(x). The online tool used to find the integration of a function is called as integration calculator.

Example 1: Find the integration of the function f(x) = (5 – x) 6

Given is the function f(x) = (5 - x) 6

Now integration of the function gives F(x)

F(x) = ∫f(x) dx = ∫(5 - x )6 dx

here let u = 5 -x;  du = -dx ; dx = -du

Now substitution gives -∫(u)6 du = -1/7[(u)6+1] = -1/7[u7]

Now u = 5 –x   (-1/7)(5 - x)7

Hence F(x) = (-1/7)(5 - x)7 + C

Example 2: Find the integration of the function f(x) = 3 cos(2x)?

Given is the function f(x) = 3 cos(2x);

Now integration of the function gives F(x)

F(x) = ∫f(x) = ∫3 cos(2x);

Here if u = 2x  du = 2dx  dx = du/2

Now substitution gives 3/2∫cosu du

[The formula of integration ∫cosx dx = sinx.]

Hence è3/2∫cosu du = 3/2 sin(u)

Now u = 2x; 3/2sin2x.

Hence F(x) = 3/2sin2x + C