Mister Exam

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How to use it?
Integral of d{x}:
Integral of x^2*e^(-x)
Integral of e^u
Integral of dx/x^3
Integral of -sinx
1-y^2
Identical expressions
one -y^ two
1 minus y squared
one minus y to the power of two
1-y2
1-y²
1-y to the power of 2
Similar expressions
1+y^2
1/(sqrt(1-y^2)*arcsin(y))
1/(sqrt(1-y^2*sin(x)^2))

Solving integrals/ 1-y^2

Integral of 1-y^2 dx

The solution

You have entered [src]

  1            
  /            
 |             
 |  /     2\   
 |  \1 - y / dy
 |             
/              
-1

$$\int\limits_{-1}^{1} \left(1 - y^{2}\right)\, dy$$

Integral(1 - y^2, (y, -1, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dy = y$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- y^{2}\right)\, dy = - \int y^{2}\, dy$
  1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int y^{2}\, dy = \frac{y^{3}}{3}$
  So, the result is: $- \frac{y^{3}}{3}$
The result is: $- \frac{y^{3}}{3} + y$
Add the constant of integration:

$- \frac{y^{3}}{3} + y+ \mathrm{constant}$

The answer is:

$- \frac{y^{3}}{3} + y+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                        3
 | /     2\              y 
 | \1 - y / dy = C + y - --
 |                       3 
/

$$\int \left(1 - y^{2}\right)\, dy = C - \frac{y^{3}}{3} + y$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

4/3

$$\frac{4}{3}$$

=

4/3

$$\frac{4}{3}$$

4/3

Numerical answer [src]

1.33333333333333

1.33333333333333

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