Integral (examples)

The methods used to find Antiderivatives are listed in the Table Of Derivatives .

Example 1

Consider the function f(x)=7. Suppose we search for

\int_3^{11} f(x) dx

.

Example 2

Consider the function

f(x)=x^4+1+2sin(x)

. Suppose we search for

\int_6^8 f(x) dx

.
:

\int f(x)dx=\int x^4dx + \int 1dx + \int2sin(x)dx

=rac{x^5}{5}+x+c-2\int-sin(x)dx

=rac{x^5}{5}+x+c-2cos(x)

\int_6^8 f(x) dx=(\int f(x)dx) f(x)dx)[6

=\left(rac{8^5}{5}+8+c-2\cos(8)
ight)-\left(rac{6^5}{5}+6+c-2\cos(6)
ight)

= +5000.408.

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