- #1
gaobo9109
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Homework Statement
How to you integrate (x2-5)1/2
Homework Equations
The Attempt at a Solution
I have tried substitution, integration by part, and none seems to work. I really don't know where to start.
gaobo9109 said:How did you get this substitution? Hyperbolic function is not in my school syllabus. Is there any other form of substitution to to solve this question?
Bohrok said:Or you could try u = √(5)secx
rahuld.exe said:use x = root5 sectheta...
i've solved it...works like a dream!...
rahuld.exe said:yeah now
5[tex]
\int tan\theta tan\theta sec\theta d\theta
[/tex]
put t = [tex] sec\theta [/tex]
therefore dt = [tex] sec\theta tan\theta d\theta [/tex]
draw a right angled triangle... using t = [tex] sec\theta[/tex].. you'll get value of two sides... find the value of the third side by pythagoras theorem... that way now you can find [tex] tan\theta [/tex]put the value of [tex] tan\theta [/tex] and dt in the integrand... solve !
rahuld.exe said:sorry i had made a mistake... i forgot the root sign... but i think this time i got it correct..
could you please check it for me...
PS: moderators... i m not posting the solution... i am actually checking if what I've done is correct...
http://img831.imageshack.us/i/p1010910lr.jpg/
The purpose of integrating (x2-5)1/2 is to find the area under the curve of the function (x2-5)1/2, also known as the antiderivative or indefinite integral. This is useful in many areas of science, such as physics, engineering, and economics.
The steps involved in integrating (x2-5)1/2 are as follows:1. Rewrite the expression as √(x2-5)2. Use the power rule for integration to find the antiderivative3. Substitute the limits of integration into the antiderivative4. Evaluate the antiderivative at the upper and lower limits5. Subtract the lower limit from the upper limit to find the final answer.
The power rule for integration states that the antiderivative of xn is (xn+1)/(n+1) + C, where C is the constant of integration. In other words, to integrate a power function, add 1 to the exponent, divide by the new exponent, and add a constant.
Yes, it is necessary to rewrite (x2-5)1/2 as √(x2-5) before integrating because the power rule for integration only applies to functions with a power of x. By rewriting the expression, we can use the power rule to find the antiderivative.
Integrating (x2-5)1/2 has many real-life applications, including finding the displacement of an object under the influence of gravity, calculating the work done by a variable force, and determining the area under a curve in economics to find the total revenue or profit. It is also used in signal processing and image reconstruction.