Help Needed: Calculus Unit Integral Block

In summary, the person is struggling with their calculus homework and asks for help with three specific problems. They are advised to integrate the slope function to find the first problem, integrate twice to find the function for the second problem, and use a u-substitution for the third problem. After some time, the person figures out their mistake and no further assistance is needed.
  • #1
scorpa
367
1
Hello Everyone,
I have been doing homework for two days straight and now I have hit a block and can't seem to get anything right. At the moment I am working on my last calculus unit- The Integral and have ground to a screeching halt :mad: I have a few questions that I was hoping someone could help me out with.

1) Determine the x-intercepts of the curve which has a slope of 2x+1 and passes through (1,-4)

2) If y' = o and y=1 when x=2 and y''-4=0, find the function

3) Find the antiderivative of x(3x^2-7)^-2dx

I just don't really know where to go with these. I am not looking for answers from all of you, I just need a boost to get me going, and explanations as to why you are doing it. My math book only gives examples and no explanations and I have to take the course by correspondance so I have no one else to help me out. Thanks for everything.
 
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  • #2
For the first,you're given the slope function.Find the function by integrating the slope.

For the second,you're given the second derivative,integrate twice and find the function.

For the third,think of some substitution that u could make.

Daniel.
 
  • #3
1) you have [itex]\frac{dy}{dx}=2x+1[/tex]

so, you set up the integral:
[tex]\int dy = \int(2x+1)dx[/tex]
solve the indefinite integral, plug in for x and y, and solve for C.

3) this a u-sub problem, where [itex]u=3x^2-7[/itex] and [itex]du=6xdx[/itex]

2) use the same concept as in #1
 
  • #4
OK thanks for the help, I figured it out last night. My problem turned out that I wasn't reading the question quite right.
 

1. What is a calculus unit integral block?

A calculus unit integral block is a specific topic or concept within the subject of calculus that involves using integrals to solve problems. It typically involves finding the area under a curve or the accumulation of change over a certain interval.

2. How is a calculus unit integral block different from other calculus topics?

A calculus unit integral block is unique in that it focuses specifically on using integrals, whereas other calculus topics may involve derivatives or other mathematical concepts. It is also a fundamental building block for more advanced calculus concepts.

3. Why is a calculus unit integral block important?

A calculus unit integral block is important because it is used in a wide range of fields, including physics, engineering, economics, and more. It allows us to solve real-world problems that involve finding areas or accumulated change, making it a crucial tool in many industries.

4. What are some common applications of calculus unit integral blocks?

Some common applications of calculus unit integral blocks include finding the area under a curve to determine distance traveled or volume of a shape, calculating work and fluid flow in physics and engineering, and analyzing changes in economic data.

5. How can I improve my understanding of calculus unit integral blocks?

To improve your understanding of calculus unit integral blocks, it is important to practice solving problems and applying the concepts to real-world scenarios. You can also seek out additional resources, such as textbooks, online tutorials, or working with a tutor or study group.

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