Integral Test
Last updated
Last updated
►Jump over to have practice at Khan academy: Integral test. Refer to article from tkiryl: The Integral Test Refer to Khan academy: Integral Test
▼Refer to awesome article from xaktly: Integral Test
Assume the series a𝖓 can be represented as a function f(x). There are a few limitations for it to use the Integral test:
f(x) MUST BE continuous.
f(x) > 0. It MUST BE a positive function.
f'(x) < 0. It's MUST BE decreasing.
The Integral test has introduced the idea of calculating the total area under the function:
The series has step of 1, which means Δx = 1
We can sum the areas (which equals the series itself):
But when we are to INTEGRATE the function area under the function:
The dx is infinitely small rather than a fixed number Δx = 1.
As result, the INTEGRAL is almost always greater than the SERIES AREAS.
Notice: DO NOT use the
Integral Testto EVALUATE series, because in general they are NOT equal.
Solve:
As been said above, we got this conclusion:
