All Calculus 2 Resources
Example Questions
Example Question #148 : Definite Integrals
First, chop up the fraction into two separate terms:
Now, integrate:
Now, evaluate at 4 and then 0. Subtract the results:
Example Question #149 : Definite Integrals
First, integrate. Remember to add one to the exponent and then also put that result on the denominator:
Now, evaluate at 3 and then 1. Subtract the results:
Simplify:
Example Question #150 : Definite Integrals
First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:
Now, evaluate at 2 and then 1:
Simplify to get your answer:
Example Question #151 : Definite Integrals
First, chop up the fraction into three separate terms:
Next, integrate:
Evaluate at 5 and then 0. Subtract the results:
Example Question #511 : Integrals
What is the integral of ?
Rewriting the integral as an easy-to-integrate indefinite integral gives us , for which we can just use the power rule to get: .
Plugging in the values gives us .
Example Question #512 : Integrals
Which of the following is ?
If we solve for the indefinite integral using the power rule, we get . If we then plug in the values, we get .
Example Question #513 : Integrals
Evaluate the definite integral
The antiderivative of is .
Using the Fundamental Theorem of Calculus,
Example Question #155 : Definite Integrals
Evaluate the definite integral
For this problem we use the fact that
As such,
Example Question #156 : Definite Integrals
Evaluate
To evaluate
we take its antiderivative and calculate . With , we get
Example Question #514 : Integrals
Evaluate
To evaluate
we take its antiderivative and calculate . With , we get
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