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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of 0dx
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Integral of -lnx
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Integral of du
- Integral of ln|x|
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Identical expressions
- sin(x/ two)*sin(nine *x/ two)
- sinus of (x divide by 2) multiply by sinus of (9 multiply by x divide by 2)
- sinus of (x divide by two) multiply by sinus of (nine multiply by x divide by two)
- sin(x/2)sin(9x/2)
- sinx/2sin9x/2
- sin(x divide by 2)*sin(9*x divide by 2)
- sin(x/2)*sin(9*x/2)dx
Integral of sin(x/2)*sin(9*x/2) dx
The solution
You have entered
[src]
1 / | | /x\ /9*x\ | sin|-|*sin|---| dx | \2/ \ 2 / | / 0
$$\int\limits_{0}^{1} \sin{\left(\frac{x}{2} \right)} \sin{\left(\frac{9 x}{2} \right)}\, dx$$
Integral(sin(x/2)*sin(9*x/2), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | /x\ /9*x\ sin(5*x) sin(4*x) | sin|-|*sin|---| dx = C - -------- + -------- | \2/ \ 2 / 10 8 | /
$${{\sin \left(4\,x\right)}\over{8}}-{{\sin \left(5\,x\right)}\over{
10}}$$
The graph
The answer
[src]
9*cos(9/2)*sin(1/2) cos(1/2)*sin(9/2)
- ------------------- + -----------------
40 40
$$-{{4\,\sin 5-5\,\sin 4}\over{40}}$$
=
=
9*cos(9/2)*sin(1/2) cos(1/2)*sin(9/2)
- ------------------- + -----------------
40 40
$$\frac{\sin{\left(\frac{9}{2} \right)} \cos{\left(\frac{1}{2} \right)}}{40} - \frac{9 \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{9}{2} \right)}}{40}$$
The graph
Use the examples entering the upper and lower limits of integration.