- #1
Ry122
- 565
- 2
How do I find the antiderivative of
(12e^2x-5)
My attempt:
u=2x-5
u'=2
12u^u x 2
24e^2x-5
What do I do next?
(12e^2x-5)
My attempt:
u=2x-5
u'=2
12u^u x 2
24e^2x-5
What do I do next?
Okay, the first step is correct.Ry122 said:How do I find the antiderivative of
(12e^2x-5)
My attempt:
u=2x-5
u'=2
12u^u x 2
24e^2x-5
What do I do next?
Ry122 said:How do I find the antiderivative of
(12e^2x-5)
My attempt:
u=2x-5
u'=2
12u^u x 2
24e^2x-5
What do I do next?
An antiderivative is the inverse operation of a derivative. It is a function that, when differentiated, gives the original function. In other words, it is the "undoing" of a derivative.
To find the antiderivative of a function, you can use the rules of integration. For example, for a function in the form of ax^n, the antiderivative would be (a/(n+1))x^(n+1). However, there are also many functions that do not follow a specific rule, and in those cases, you would need to use other techniques such as substitution or integration by parts.
The process for finding the antiderivative of (12e^2x-5) would involve using the rules of integration. Since the function contains an exponential term, we would need to use the rule for integrating exponential functions, which is ∫e^x dx = e^x + C. Then, we would need to apply the constant multiple rule, which states that ∫af(x) dx = a∫f(x) dx. Combining these rules, the antiderivative of (12e^2x-5) would be 12∫e^2x dx - 5∫1 dx = 12(e^2x)/2 - 5x + C = 6e^2x - 5x + C.
Yes, most scientific calculators have a built-in function to find the antiderivative of a given function. However, it is important to note that calculators may not be able to handle more complex functions, so it is important to also know how to find the antiderivative using integration rules and techniques.
Finding the antiderivative is important in science because it allows us to find the original function from its derivative. This is useful in many scientific fields, such as physics and engineering, where knowing the original function can help in solving problems and making predictions. It also plays a crucial role in calculus, which is a fundamental concept in many scientific disciplines.