Calculus 2 : Definite Integrals
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Example Questions
Example Question #101 : Finding Integrals
If 
First off, you're going to want to integrate the derivative to get the original function.
When integrating, raise the exponent by 1 and put that result on the denominator.
Therefore, the integral is
Remember to add a C because it is an indefinite integral at this point.
To find C, plug in 1 for x and set the integral equal to 2 from your initial conditions:
Plug 2 in for C to get your function:
Example Question #103 : Finding Integrals
If 
Recall that the integral of acceleration is velocity.
Therefore, integrate the acceleration function first. Recall that you raise the exponent by 1 and then put that result on the denominator.
Therefore,
Remember to add a +C because it is an indefinite integral.
Then, plug in your initial conditions to find C:
Plug your value in for C to get an answer of
Example Question #104 : Finding Integrals
Evaluate.
Answer not listed.
In this case, 
The antiderivative is 
Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:
Example Question #105 : Finding Integrals
Evaluate.
Answer not listed.
In this case, 
The antiderivative is 
Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:
Example Question #101 : Finding Integrals
Evaluate.
Answer not listed.
In this case, 
The antiderivative is 
Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:
Example Question #101 : Finding Integrals
Evaluate.
Answer not listed.
In this case, 
The antiderivative is 
Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:
Example Question #111 : Finding Integrals
Evaluate.
Answer not listed.
Answer not listed.
In this case, 
The antiderivative is 
Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:
Example Question #111 : Finding Integrals
Evaluate.
Answer not listed.
In this case, 
The antiderivative is 
Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:
Example Question #111 : Finding Integrals
First, integrate the expression. Remember to raise the exponent by 1 and then put that result on the denominator as well: 
Example Question #112 : Finding Integrals
First, integrate the expression. Remember to raise the exponent by 1 and then also put that result on the denominator.
Therefore, after integrating, it should look like:
Then, first evaluate at 4 and then 0.
Subtract the results:
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