How to prove f(a) is integrable?

  • Thread starter Thread starter ak123456
  • Start date Start date
ak123456
Messages
50
Reaction score
0

Homework Statement


f(a)=a^2 on the interval [0,1],how to prove it by the definition of integral ,and to find \intf(a) on the interval [0,1]



Homework Equations





The Attempt at a Solution


to prove by step functions ? set ai= (i/n)^(1/2) ??
 
Physics news on Phys.org
What is the definition of integrability you are using?
 
icantadd said:
What is the definition of integrability you are using?

Riemann integrability
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Improper integral convergence from 0 to 1
Replies
13
Views
3K
If A is dense in [0,1] and f(x) = 0, x in A, prove ∫fdx = 0.
Replies
2
Views
2K
Let function ƒ be Differentiable
Replies
2
Views
1K
Proving Injectivity of Shroeder-Berstein Theorem for R to R^2 x R^2
Replies
5
Views
2K
Showing that a pathological function is only continuous at 0
Replies
7
Views
2K
Integral of x^n using Reimann sums
Replies
4
Views
1K
Problem involving recursion theorem
Replies
11
Views
1K
Taylor polynomial, approximative solution of this equation
Replies
3
Views
1K
Solving the Minimization Operator Problem
Replies
19
Views
2K
Centroid calculation using integrals
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top