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Chipset3600
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Hello MHB, how can i solve this without use integration technniques...
[TEX]\int tan(t)sec^3(t)dt[/TEX]
[TEX]\int tan(t)sec^3(t)dt[/TEX]
Chipset3600 said:Hello MHB, how can i solve this without use integration technniques...
[TEX]\int tan(t)sec^3(t)dt[/TEX]
SuperSonic4 said:How do you mean "without using integration techniques"? Surely you need integration techniques to solve an integral? Also what have you tried?
Hint: Let $u = \sec(t) = \frac{1}{\cos(t)}$
How can i solve this without use integration technniques?
. . [TEX]\int \tan\theta \sec^3\!\theta\,d\theta[/TEX]
soroban said:Hello, Chipset3600!
Well, maybe you can see all this?If we have: .[tex]f(x) \:=\:\tfrac{1}{3}\sec^3\!\theta + C[/tex]
Then: .[tex]f'(x) \:=\:\tfrac{1}{3}\cdot 3\sec^2\!\theta\cdot\sec\theta\tan\theta + 0 \;=\;\tan\theta\sec^3\!\theta [/tex]
An integral without using integration technique is a mathematical concept that represents the area under a curve without using traditional integration methods. It is often used as an alternative method for finding the area under a curve when traditional integration techniques are not applicable.
An integral without using integration technique is typically calculated by dividing the area under the curve into smaller, simpler shapes, such as rectangles or triangles. The area of each shape is then calculated individually and added together to approximate the total area under the curve.
One limitation of using an integral without integration technique is that it can only approximate the area under a curve, rather than providing an exact value. Additionally, this method may not work for more complex functions or curves with irregular shapes.
The main difference between an integral without using integration technique and traditional integration methods is the approach used to calculate the area under a curve. While traditional integration methods involve finding the antiderivative of a function, an integral without integration technique uses geometric shapes to approximate the area.
An integral without using integration technique may be beneficial in situations where traditional integration methods are not applicable or too complex. This method can also be useful for quickly estimating the area under a curve, as it does not require advanced mathematical knowledge or complex calculations.