How do I calculate an integral with a square root in the denominator?

In summary, an integral calculation is a mathematical technique used to find the area under a curve or the volume of a solid. It differs from a derivative in that it calculates the accumulation of change over an interval rather than the instantaneous rate of change. There are two main types of integrals: definite and indefinite. The fundamental theorem of calculus states that differentiation and integration are inverse operations. In real-life applications, an integral calculation is used in various fields to solve problems involving rates of change and calculate physical quantities.
  • #1
solkahns
1
0
Hi,
I have a problem. I can't understand how it becomes [-1/the square root of (z^2+r^2)] from integral (r.dr/(z^2+r^2)^3/2)
It seems complicated but I couldn't write it different.
Thanks, Sol
P.S. The integral goes to R from 0.
 
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  • #2
It's a simple u-substitution. Try to do it, and come back if you get stuck.
 
  • #3
[tex]\frac{d}{dr}(-\frac{1}{(z^{2}+r^{2})^{\frac{1}{2}}})=\frac{1}{2}*\frac{1}{(z^{2}+r^{2})^{\frac{3}{2}}}*2r=\frac{r}{(z^{2}+r^{2})^{\frac{3}{2}}}[/tex]
That's all there is to it, really..
 

FAQ: How do I calculate an integral with a square root in the denominator?

What is an integral calculation?

An integral calculation is a mathematical technique used to find the area under a curve or the volume of a solid. It involves breaking down a complex shape into smaller, simpler shapes and adding up their areas or volumes to find the total.

How is an integral calculation different from a derivative?

While a derivative measures the instantaneous rate of change of a function, an integral calculates the accumulation of change over a certain interval. In other words, a derivative tells us the slope of a curve at a specific point, while an integral tells us the total amount of change that has occurred over a given interval.

What are the different types of integrals?

There are two main types of integrals: definite and indefinite. A definite integral has specific limits of integration and gives a precise numerical value. An indefinite integral does not have limits of integration and instead gives a general formula for the area under a curve.

What is the fundamental theorem of calculus?

The fundamental theorem of calculus states that differentiation and integration are inverse operations. This means that if we take the derivative of an integral, we will get back the original function, and vice versa.

How is an integral calculation used in real-life applications?

An integral calculation is used in many areas of science, engineering, and economics to solve problems involving rates of change, such as finding the velocity of a moving object or the growth rate of a population. It is also used in physics to calculate work, energy, and other physical quantities.

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