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Suppose that int_{0}^{1} f(t)dt =7. Calculate each of the following. a. int_{0}^{1} f(10t)dt = b....

Question:

Suppose that {eq}\int_{0}^{1} f(t)dt =7 {/eq}. Calculate each of the following.

{eq}a. \int_{0}^{1} f(10t)dt =\\ b. \int_{0}^{1} f(1-10t)dt =\\ c. \int_{0}^{1} f(5-4t)dt = {/eq}

Substitution with Unknown Function:

If we have an integer value of the given definite integral expression with unknown function, then we'll rearrange all the other definite integral expressions as the given expression using the substitution method.

For that, we'll substitute the variable of the unknown function by the variable {eq}u {/eq} and differentiate the substitution to replace the {eq}dt {/eq} term of the given integral expression.

Answer and Explanation:

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a.

The given value of the definite

{eq}\int_{0}^{1} f(t)dt =7 {/eq}

We can write the above expression as:

{eq}\int_{0}^{1} f(u) \ du =7 {/eq}

{...

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How to Solve Integrals Using Substitution

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Chapter 13 / Lesson 5
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