Mister Exam

Other calculators

dt/sqrt(25-t^2)
Solving integrals/ dt/sqrt(25-t^2)

Integral of dt/sqrt(25-t^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dt
 |     _________   
 |    /       2    
 |  \/  25 - t     
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{25 - t^{2}}}\, dt$$ 
Integral(1/(sqrt(25 - t^2)), (t, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=5*sin(_theta), rewritten=1, substep=ConstantRule(constant=1, context=1, symbol=_theta), restriction=(t > -5) & (t < 5), context=1/(sqrt(25 - t**2)), symbol=t)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                        
 |                                                         
 |      1                //    /t\                        \
 | ------------ dt = C + | -5, t < 5)|
 |    _________          \\    \5/                        /
 |   /       2                                             
 | \/  25 - t                                              
 |                                                         
/
$$\int \frac{1}{\sqrt{25 - t^{2}}}\, dt = C + \begin{cases} \operatorname{asin}{\left(\frac{t}{5} \right)} & \text{for}\: t > -5 \wedge t < 5 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
asin(1/5)
$$\operatorname{asin}{\left(\frac{1}{5} \right)}$$ 
=
= 
asin(1/5)
$$\operatorname{asin}{\left(\frac{1}{5} \right)}$$ 
asin(1/5)
Numerical answer [src] 
0.201357920790331
0.201357920790331
The graph
Integral of dt/sqrt(25-t^2) dx

    Use the examples entering the upper and lower limits of integration.

    © Mister Exam – Calculator