Mister Exam

Other calculators

Solving integrals/ -sin(t)*cos(t)

Integral of -sin(t)*cos(t) dt

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                  
 --                  
 4                   
  /                  
 |                   
 |  -sin(t)*cos(t) dt
 |                   
/                    
0
$$\int\limits_{0}^{\frac{\pi}{4}} - \sin{\left(t \right)} \cos{\left(t \right)}\, dt$$ 
Integral((-sin(t))*cos(t), (t, 0, pi/4))
Detail solution

  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

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

        1. The integral of is when :

        So, the result is:

      Now substitute back in:

    Method #2

    1. Let .

      Then let and substitute :

      1. The integral of is when :

      Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                           2   
 |                         sin (t)
 | -sin(t)*cos(t) dt = C - -------
 |                            2   
/
$$\int - \sin{\left(t \right)} \cos{\left(t \right)}\, dt = C - \frac{\sin^{2}{\left(t \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-1/4
$$- \frac{1}{4}$$ 
=
= 
-1/4
$$- \frac{1}{4}$$ 
-1/4
Numerical answer [src] 
-0.25
-0.25

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

    © Mister Exam – Calculator