Calculus 1 : How to find integral expressions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #141 : How To Find Integral Expressions

Evaluate the following integral:

Possible Answers:

Correct answer:

Explanation:

To evaluate the integral, we must first make the following substitution:

Now, rewrite the integral and integrate:

The integration was performed using the following rules:

Finally, replace u with our original x term:

Example Question #142 : How To Find Integral Expressions

Evaluate the following integral:

Possible Answers:

Correct answer:

Explanation:

The integral is equal to

and was evaluated using the following rules:

Example Question #141 : How To Find Integral Expressions

Integral

If is even,

Possible Answers:

None of the above

It is called differentiating odd functions

The statement is true

The statement is false

It is called differentiating even functions

Correct answer:

The statement is true

Explanation:

According to the integration of even function rule,

Example Question #143 : How To Find Integral Expressions

Write the integral expression for the area under the following curve from  to .

Possible Answers:

Correct answer:

Explanation:

To write the integral expression, simply set the bounds given with the smaller on the bottom and don't forget the . Thus,

Example Question #145 : How To Find Integral Expressions

Find the integral of the following equation from  to .

Possible Answers:

Correct answer:

Explanation:

To solve, simply plug in your bounds and equation. Make sure to note how the order of bounds was said in the problem. Thus,

Example Question #144 : How To Find Integral Expressions

Evaluate the following integral:

Possible Answers:

Correct answer:

Explanation:

To evaluate the integral, we must perform the following subsitution:

The derivative was found using the following rule:

Now, rewrite the integral and integrate:

The integral was found using the following rule:

Finally, replace u with the original term:

Example Question #147 : How To Find Integral Expressions

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

To find the integral, first find the antiderivative, then evaluate at the limits of integration to find the definite integral.

Here, the antiderivative is .

Example Question #142 : Integral Expressions

Integrate:

Possible Answers:

Correct answer:

Explanation:

When integrating this expression, tackle each term separately. For , leave the  out and just integrate the  term. Raise the exponent by  and then put that result on the denominator: . Do that for each term.  becomes and  becomes . Put those all together and add a "C" at the end because it is an indefinite integral: .

Example Question #145 : How To Find Integral Expressions

Possible Answers:

Correct answer:

Explanation:

Before integrating this expression, I would chop it up into three separate terms and simplify since there is only one term on the denominator: . Then, integrate each term separately. When you integrate, you raise the exponent by  and then put that result on the denominator. Therefore, the resulting expression after integrating is: . Simplify and add a "C" at the end (it's an indefinite integral) and the answer is:

.

Example Question #146 : How To Find Integral Expressions

Possible Answers:

Correct answer:

Explanation:

First, just focus on integrating the expression before evaluating it. When integrating, raise the exponent by one and then put that result on the denominator. Therefore, after integrating, you get: . Then, plug in , which yields  and then subtract the result of when you plug in .

.

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