Area Between a Graph and a Line: How Do We Find It?

  • Thread starter Thread starter intenzxboi
  • Start date Start date
  • Tags Tags
    Area Graph
intenzxboi
Messages
98
Reaction score
0

Homework Statement


Find area between
f(x) = 1 / 1+x^2 and the line y= 1/2


The Attempt at a Solution



would i need to take the anti derivative of it then minus 1/2??
 
Physics news on Phys.org
You'll need to use a definite integral, and the antiderivative is involved in the definite integral. You'll need limits of integration, too.

Have you graphed the region whose area you're trying to find? That would be a good start.
 
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...

Similar threads

Replies
7
Views
2K
Replies
12
Views
2K
Replies
2
Views
1K
Replies
18
Views
2K
Replies
5
Views
2K
Replies
1
Views
2K
Replies
2
Views
2K
Back
Top