Calculus 1 : How to find integral expressions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #1081 : Functions

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Using the Power Rule  (), take the anti-derivative:

Next, evaluate the integral at the given points:

 

Example Question #1082 : Functions

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Using the Power Rule  (), take the antiderivative:

Next, evaluate the integral at the given points:

 

Example Question #1083 : Functions

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Using the Power Rule  (), take the anti-derivative then plug in for the interval given: 

Example Question #31 : Equations

Integrate .

Possible Answers:

Correct answer:

Explanation:

Using the Power Rule  (), take the anti-derivative:

 

Example Question #35 : Integral Expressions

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Using the Power Rule  (), take the anti-derivative:

Example Question #31 : Integral Expressions

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Take the anti-derivative (integrate using the Power Rule : ) of the expression:

Example Question #1084 : Functions

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Take the anti-derivative (integrate using the Power Rule : ) of the expression: 

Example Question #1081 : Functions

If  is defined as , what is ?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given the derivative , we can find the function  by indefinitely integrating  in accordance with the Power Rule for Integrals: , where  and  is the arbitrary constant of integration. 

Using this rule, we therefore know that .

Example Question #39 : Integral Expressions

If  is defined as , what is ?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given the derivative , we can find the function  by indefinitely integrating  in accordance with the Power Rule for Integrals: , where  and  is the arbitrary constant of integration. 

Using this rule, we therefore know that .

Example Question #1091 : Functions

If  is defined as , what is ?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given the derivative , we can find the function  by indefinitely integrating  in accordance with the Power Rule for Integrals: , where  and  is the arbitrary constant of integration. 

Using this rule, we therefore know that .

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