Solving Integral 0 to 3 f(3t)dt Given Question Info

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In summary, an integral is a mathematical concept used to calculate the area under a curve on a graph and the total change of a quantity over a specific interval. The notation "0 to 3" in an integral represents the interval being integrated over, while f(3t) represents the function being integrated. To solve an integral, one must find an antiderivative of the function and evaluate it at the limits of integration using techniques such as substitution or integration by parts. Using u-substitution, multiplying the x-values of the function by a constant like 3 can simplify the integral and make it easier to solve.
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sapiental
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There was a question on my quiz today that went something like this

the integral 0 to 5 f(x)dx = 7, the integral 1 to 5 f(x)dx = 3

given this information, solve the integral 0 to 3 f(3t)dt.

I had no idea how to do it... How can I compute f(3t)dt given this information? or does the t = x?

Thanks
 
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Think of what kind of function f(3t) is. Try to compare it with the function f(x).
 

FAQ: Solving Integral 0 to 3 f(3t)dt Given Question Info

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to calculate the total change or accumulation of a given quantity over a specific interval.

2. What is the meaning of "0 to 3" in the integral?

The "0 to 3" represents the interval over which the function is being integrated. In this case, it means that we are finding the area under the curve from 0 to 3 units on the x-axis.

3. What does f(3t) represent in the integral?

The function f(3t) represents the curve that is being integrated. It is important to note that this function is being evaluated at 3t, which means that the x-values of the function are being multiplied by 3 before being integrated.

4. How do you solve an integral?

Solving an integral involves finding an antiderivative of the function being integrated, and then evaluating it at the limits of integration. This can be done using integration techniques such as substitution, integration by parts, or by using tables of integrals.

5. Why is the question asking for the integral of f(3t) instead of just f(t)?

This is a common technique in integral calculus known as u-substitution. By multiplying the x-values of the function by 3, we are able to simplify the integral and make it easier to solve. It is a useful tool for solving integrals involving more complex functions.

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