All Calculus 2 Resources
Example Questions
Example Question #31 : Indefinite Integrals
When integrating, we do the opposite of a derivative. You increase the exponent by one and divide the function by that new power. Since this is an indefinite integral, we have to add a
at the end of the equation.
Example Question #2402 : Calculus Ii
The antiderivative of
. The antiderivative of . Remember, this is the opposite of a derivative. Therefore, for our integral, we have:.
Example Question #2403 : Calculus Ii
Example Question #32 : Indefinite Integrals
Find
Using integration by parts:
Example Question #662 : Integrals
Euler's identity states that:
Also recall that:
Determine
To determine the integral we just do
substitution:
By the fundamental theorem of calculus:
Example Question #33 : Indefinite Integrals
Determine:
Doing integration by parts twice:
Example Question #37 : Indefinite Integrals
Determine
Using
substitution,
Example Question #34 : Indefinite Integrals
Evaluate the following Definite Integral:
Upon early inspection of this problem, two things may be seen immediately: a trigonometric function and a composite function. One may notice that
is the derviative of , this urges us to use the u-substitution method.Let
, therefore the problem may be rewritten as:, this is a known trigonometric integral to be , when plugging in for u, the final answer is: .
Example Question #664 : Integrals
An identity of
is given by:, where is the imaginary number
Determine :
Using the definition above:
This reduces to:
Example Question #36 : Indefinite Integrals
Calculate the following integral:
In progress
We can use integration by parts to solve this integral
Integration by parts states:
Let u =
and dv=Thus, our integral becomes:
Which simplifies to:
, which equals : , giving us our answerCertified Tutor
Certified Tutor
All Calculus 2 Resources
