Mister Exam

Other calculators

Solving integrals/ ysinx

Integral of ysinx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  y*sin(x) dx
 |             
/              
0
∫01ysin⁡(x) dx\int\limits_{0}^{1} y \sin{\left(x \right)}\, dx 
Integral(y*sin(x), (x, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫ysin⁡(x) dx=y∫sin⁡(x) dx\int y \sin{\left(x \right)}\, dx = y \int \sin{\left(x \right)}\, dx

    1. The integral of sine is negative cosine:

      ∫sin⁡(x) dx=−cos⁡(x)\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}

    So, the result is: −ycos⁡(x)- y \cos{\left(x \right)}

  2. Add the constant of integration:

    −ycos⁡(x)+constant- y \cos{\left(x \right)}+ \mathrm{constant}

The answer is:

−ycos⁡(x)+constant- y \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
 |                           
 | y*sin(x) dx = C - y*cos(x)
 |                           
/
−cos⁡x y-\cos x\,y
Simplify
The answer [src] 
y - y*cos(1)
(1−cos⁡1) y\left(1-\cos 1\right)\,y 
=
= 
y - y*cos(1)
−ycos⁡(1)+y- y \cos{\left(1 \right)} + y
Simplify

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

    © Mister Exam – Calculator