Jbreezy said:Homework Statement
Hey I'm doing something really stupid it is really pissing me off why I can't figure it out.
The Attempt at a Solution
Evaulate the integral : ∫ x(1-x)^1/2
I tried with substitution. u = 1-x , -du = dx and x = 1-u
∫ (1-u)(u)^1/2 I just tried to simplify it some.
∫ (u^1/2-u^3/2) -du
-∫ u^1/2 du +∫ u^3/2 du
integrate I got
(-2/3)u^ 3/2 + (2/5)u^5/2
(-2/3)(1-x)^ 3/2 + (2/5)(1-x)^5/2
My book got (-2/15)*2+3x)(1-x)^3/2 + C
I'm lost.
Thanks for the help.
Integration in Calculus 1 can be challenging because it requires a deep understanding of the fundamental concepts of differentiation, as well as knowledge of various integration techniques and applications.
There are several techniques that can be used to solve integration problems, such as u-substitution, integration by parts, trigonometric substitutions, and partial fraction decomposition. Additionally, practicing with different types of integration problems can also help improve problem-solving skills.
One way to avoid mistakes when integrating is to carefully check each step of your work and make sure that it aligns with the rules of integration. It is also helpful to practice regularly and review the fundamental concepts of integration.
Some integration problems may require multiple steps because they may involve more complex functions and require the use of integration techniques such as u-substitution or integration by parts. It is important to break down the problem into smaller, manageable steps to avoid making mistakes.
One way to improve integration skills is to practice regularly with different types of integration problems and review the fundamental concepts and rules. It may also be helpful to seek additional resources, such as tutoring or online tutorials, to gain a better understanding of the subject.