PROPERTIES OF DEFINITE INTEGRALS

Property 1 :

If the limits of integration are the same, the integral is just a line and contains no area.

Property 2 :

If the limits are reversed, then place a negative sign in front of the integral.

Property 3 :

The integral of a sum is the sum of the integrals.

Property 4 :

The integral of a difference is the difference of the integrals.

Property 5 :

The integral of the product of a constant 'c' and a function f(x) is equal to the constant multiplied by the integral of the function.

Property 6 :

Although this formula normally applies when c is  between a and b (a < x < b), the formula holds for all values of a, b, and c, provided f(x) is integrable on the largest interval.

Property 7 :

For the same function and same limits, if the variable is changed, the result of a definite integral will not change.

Property 8 :

In a function f(x),

f(-x) = -f(x) ----> f(x) is an odd function

f(-x) = f(x) ----> f(x) is an even function

If f(x) is an odd function,

If f(x) is an even function,

Property 9 :

If f(a + x) = f(x), f(x) is a period function with the period is a.

Property 10 :

Let k = a⁵ and u = x⁵.

ᵈᵘ⁄dₓ = 5x⁴

⅕du = x⁴dx

Formula :

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