Mister Exam

Other calculators

t^3sin(2t^4)dt
Solving integrals/ t^3sin(2t^4)dt

Integral of t^3sin(2t^4)dt dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |   3    /   4\     
 |  t *sin\2*t /*1 dt
 |                   
/                    
0
∫01t3sin⁡(2t4)1 dt\int\limits_{0}^{1} t^{3} \sin{\left(2 t^{4} \right)} 1\, dt 
Integral(t^3*sin(2*t^4)*1, (t, 0, 1))
Detail solution

  1. Let u=2t4u = 2 t^{4}.

    Then let du=8t3dtdu = 8 t^{3} dt and substitute du8\frac{du}{8}:

    ∫sin⁡(u)64 du\int \frac{\sin{\left(u \right)}}{64}\, du

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

      ∫sin⁡(u)8 du=∫sin⁡(u) du8\int \frac{\sin{\left(u \right)}}{8}\, du = \frac{\int \sin{\left(u \right)}\, du}{8}

      1. The integral of sine is negative cosine:

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

      So, the result is: −cos⁡(u)8- \frac{\cos{\left(u \right)}}{8}

    Now substitute uu back in:

    −cos⁡(2t4)8- \frac{\cos{\left(2 t^{4} \right)}}{8}

  2. Add the constant of integration:

    −cos⁡(2t4)8+constant- \frac{\cos{\left(2 t^{4} \right)}}{8}+ \mathrm{constant}

The answer is:

−cos⁡(2t4)8+constant- \frac{\cos{\left(2 t^{4} \right)}}{8}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
 |                            /   4\
 |  3    /   4\            cos\2*t /
 | t *sin\2*t /*1 dt = C - ---------
 |                             8    
/
−cos⁡(2 t4)8-{{\cos \left(2\,t^4\right)}\over{8}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901-1
Plot the graph f(x)
The answer [src] 
1   cos(2)
- - ------
8     8
18−cos⁡28{{1}\over{8}}-{{\cos 2}\over{8}} 
=
= 
1   cos(2)
- - ------
8     8
−cos⁡(2)8+18- \frac{\cos{\left(2 \right)}}{8} + \frac{1}{8}
Simplify
Numerical answer [src] 
0.177018354568393
0.177018354568393
The graph
Integral of t^3sin(2t^4)dt dx

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

    © Mister Exam – Calculator