Calculus 2 : Definite Integrals

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #534 : Integrals

Possible Answers:

Correct answer:

Explanation:

First, integrate. Remember to add one to the exponent and also put that result on the denominator:

Now, evaluate at 4 and then 1. Subtract the results:

Simplify to get your answer:

Example Question #535 : Integrals

Possible Answers:

Correct answer:

Explanation:

First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:

Evaluate at 2 and then 0. Subtract the results:

Example Question #536 : Integrals

Possible Answers:

Correct answer:

Explanation:

First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:

Now, evaluate at 2 and then at 1. Subtract the results:

Simplify to get your answer:

Example Question #537 : Integrals

Possible Answers:

Correct answer:

Explanation:

Step 1: Integrate:



Step 2: Evaluate at the upper limit:

Plug in .



Step 3: Evaluate at the lower limit:

Plug in .



Step 4: Take the valuation at the lower limit and subtract it FROM the upper limit:



The integration of  is 


Example Question #538 : Integrals

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Step 1: Take the antiderivative of each term:


 



Step 2: Put all the antiderivatives in step 1 together based on the signs in the integral...



Step 3: Plug in the upper and lower limits:

Upper Limit is , lower limit is .

Plug in :



Plug in . Since all terms have , the value will be 

Step 4: Subtract the value of the lower limit from the upper limit:



The value of this integral is .

Example Question #539 : Integrals

Possible Answers:

Correct answer:

Explanation:

First, integrate this expression. Remember to raise the exponent by 1 and then also put that result on the denominator:

Now, evaluate at 2 and then 0. Subtract the results:

Simplify to get your answer:

Example Question #540 : Integrals

Possible Answers:

Correct answer:

Explanation:

First, take the 4 outside of the integral sign and rewrite the radical as a fractional exponent. It's easier to visualize that when integrating:

Now integrate. Remember to raise the exponent by 1 and also put that result on the denominator:

Simplify and multiply by the 4 that you took out:

Now evaluate at 2 and then 0. Subtract the results:

Example Question #171 : Definite Integrals

Possible Answers:

Correct answer:

Explanation:

First, integrate. Remember to add one to the exponent and also put that result on the denominator:

Now, evaluate at 2 and then 1. Subtract the results:

Example Question #172 : Definite Integrals

Possible Answers:

Correct answer:

Explanation:

First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:

Now, evaluate at 4 and then 1. Subtract the results:

Simplify to get your answer:

Example Question #173 : Definite Integrals

Possible Answers:

Correct answer:

Explanation:

First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:

Now evaluate at 4 and then 2. Subtract the results:

Simplify to get your answer:

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