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If a function f(x) is continuous on a given interval, then the method of integration gives the area under graph of the particular function f(x). Integral of a function is in fact the anti-derivative of the function and Integral calculator is a tool used to find the integral of the function with respect to a variable.

**Example 1:Find the integration of the function, f(x) = 7x3 + 4x2 – 5x + 2.**

In order to find the integral, the **Power Rule** says:

**∫x**^{n} dx= x^{(n+1)}/ (n+1) + c where ‘c’ is a constant!

Following this rule, we can apply the above formula for every exponent in the function.

∫(fx) dx = 7* x^{3+1}/(3+1) + 4* x^{2+1}/(2+1) –5* x^{1+1}/(1+1) + 2*x + c

**∫ f(x) dx = 7x**^{4/ }4 + 4x^{3}/ 3 – 5x^{2}/ 2 + 2x + c

Following this rule, we can apply the above formula for every exponent in the function.

∫(fx) dx = 7* x

Anti-derivative is the same meaning as finding integral of a function.

Here we have a trigonometric function and we know the fact that derivative of the trigonometric function cos(x) is –sin(x), so we have the opposite interpretation for the integral of it.

So the anti-derivative of sin(x) function is – cos(x).

**∫ sin(x) dx = - cos(x) + c**

Now ∫ (sin2x) dx = - cos( 2x) / 2 + c

Here we have a trigonometric function and we know the fact that derivative of the trigonometric function cos(x) is –sin(x), so we have the opposite interpretation for the integral of it.

So the anti-derivative of sin(x) function is – cos(x).

Now ∫ (sin2x) dx = - cos( 2x) / 2 + c